## CBSE_class X time bound sample paper 4 marks Trigonometry_Solutions

Here are the solutions for your reference. In case of any queries  do drop your questions so that it can be answered in time.

Ans 1 .  given 3x = cosecA, 3/x = cotA

$=3[ x^2 - 1/x^2 ]$

$=3x^2 - 3/x^2$

$=1/3[ 9x^2 - 9/x^2]$    (multiply and divide by 3 )

$=1/3[ {3x}^2 - {3/x}^2 ]$

$=1/3[ cosec^2A - cot^2A ]$    (identity 3)

$=1/3 * 1$

$=1/3$

Ans 2 .  given 6x = secB , 6/x = tanB

$= 9 [ x^2 - 1/x^2 ]$

$= 9 * 36/36 [ x^2 - 1/x^2 ]$    ( multiply and divide by 36)

$= 9 /36 [ (6x)^2 - (6/x)^2 ]$

$= 1/4 [ sec^2B - tan^2B ]$      (substituting the values of 6x and 6/x)

$= 1/4 [ 1]$     ( identity 2 )

$= 1/4$

Ans 3 . Given

$x.sin^3A + y.cos^3A = sinA.cosA ..............eq(1)$

$, x.sinA = y.cosA ..................eq(2)$

$x = y.cosA / SinA$

substituting in eq(1).

$y.cosA/sinA . sin^3A + y.cos^3A = sinA.cosA$

$y.cosA.sin^2A + y.cos^3A = sinA.cosA$

$y.cosA ( sin^2A + cos^2A) = sinA.cosA$

$y.cosA. (1) = sinA.cosA$

$y = sinA$

$x = sinA. cosA/sinA$

$x = cosA$

$L.H.S = x^2 + y^2$

$= sin^2A + cos^2A$  (identity 1)

$= 1$

Hence L.H.S = R.H.S

Ans 4.

$LHS = [ cos^2 A/ cos^2B + cos^2 A / sin^2B ] . cos^2B$

$= cos^2A [ 1/cos^2B + 1/sin^2B ]. cos^2B$

$= cos^2A[ (sin^2B + cos^2B) / (cos^2B.sin^2B) ]. cos^2B$

$= cos^2A. 1. cos^2B / cos^2B.sin^2B$

$= cos^2A / sin^2B$

$= n^2$

$= RHS$

Ans 5.

$LHS = ( m^2 - n^2 )^2$

$= [( tanA + sinA )^2 - ( tanA - sinA )^2 ]^2$

$= [ tan^2A + sin^2A + 2.sinA.tanA - ( tan^2A + sin^2A - 2.sinA.tanA ) ]^2$

$= [ tan^2A + sin^2A + 2.sinA.tanA - tan^2A - sin^2A + 2.sinA.tanA ) ]^2$

$= [ 4.sinA.tanA ]^2$

$= 16.tan^2A.sin^2A$

$= 16.tan^2A.(1 - cos^2A )$

$= 16.[tan^2A - tan^2A. cos^2A ]$

$= 16.[tan^2A - ( sin^2A / cos^2A ). cos^2A ]$

$= 16.[tan^2A - sin^2A )$

$= 16.( tanA + sinA ).( tanA - sinA )$

$= 16.m.n$

$= RHS$

Ans 6.

$LHS = ( p^2 +1 ).cosA$

$= [ ( cosecA + cotA )^2 +1 ].cosA$

$= [ cosec^2A + cot^2A + 2.cosecA.cotA +1 ].cosA$

$= [ cosec^2A + cosec^2A + 2.cosecA.cotA ].cosA$   ( identity 2 )

$= [ 2.cosec^2A + 2.cosecA.cotA ].cosA$

$= [ 2.cosecA( cosecA + cotA ].cosA$

$= [ 2.cosA/sinA ( cosecA + cotA ]$

$= [ 2.cotA ( cosecA + cotA ]$

$= 2.cotA . cosecA + 2.cot^2A$

$= 2.cotA . cosecA + .cot^2A + cot^2A$

$= 2.cotA . cosecA + .cot^2A + cosec^2A - 1$

$= ( cosecA + .cotA )^2 - 1$

$= p^2 - 1$

$= RHS$

Ans 7.

$cosA = 2m/(m^2 + 1)$

$sin^2A = 1 - cos^2A$

$sin^2A = 1 - [ 2m/(m^2 + 1 ) ]^2$

$sin^2A = [ (m^2 + 1)^2 - 4m^2 ] / ( m^2 + 1 )^2$

$sin^2A = [ (m^2 + 1 +2m) ( m^2 + 1 -2m ) ] / ( m^2 + 1 )^2$

$sin^2A = [ (m + 1 )^2 ( m - 1 )^2 ] / ( m^2 + 1 )^2$

$sinA =$$[ (m + 1 )^2 ( m - 1 )^2 ] / ( m^2 + 1 )^2$

$sinA = ( m^2 - 1 ) / ( m^2 + 1 )$

$tanA = sinA / cosA$

$tanA = [(m^2 -1) / (m^2 + 1 ) ] / [ 2m / (m^2 + 1) ]$

$tanA = (m^2 - 1) / 2m$

$cosecA = (m^2 + 1) / (m^2 - 1 )$

$cotA = 2m / (m^2 - 1)$

Ans 8.

given tanA = p/q

LHS = (psinA – qcosA ) / (psinA + qcosA)

dividing both numerator and denominator by qcosA

$= [ p.sinA/q.cosA - 1 ] / [ p.sinA / q.cosA + 1 ]$

$= [ p.tanA/q - 1 ] / [ p.tanA/ q + 1 ]$

$= [ p^2/q^2 - 1 ] / [ p^2/ q^2 + 1 ]$

$= [ (p^2-q^2) / q^2 ] / [ (p^2 + q^2) / q^2 ]$

$= (p^2-q^2) / (p^2 + q^2)$

$= RHS$

hence proved.

Ans 9.

Given tan B = a/b

= (a sinB + bcosB) / (a sinB – bcosB)

dividing both numerator and denominator by bcosB

$= (a/b .tanB + 1) / (a/b tan B - 1)$

$= (a^2/b^2 + 1) / (a^2/b^2 - 1)$

$= (a^2 + b^2 ) / (a^2 - b^2 )$

Ans 10.

given x = a Cos³A  y = b Sin³A

$LHS = [ x / a ] ^2/3 + [ y / b ] ^ 2/3$

$= [ acos^3A/ a ] ^2/3 + [ bsin^3A / b ] ^ 2/3$

$= cos ^2A + sin ^ 2A$     ( identity 1)

$= 1$

## CBSE_class X time bound sample paper 4 marks Trigonometry

Students must ensure that below questions must be attempted in the limited time of 40 mins.

Else Answer sheet will not be corrected.  This is the time bound test to ensure your understanding

about the chapter and thorough revision.

Q 1. If 3x = Cosec A and 3/x = Cot A, find the value of  $3[x^2 - 1/x^2]$.

Q 2. If  6x = Sec B and 6/x = tan B , find the value of $9[x^2 - 1/ x^2]$.

Q 3. If $x.sin^3 A + y. cos^3 A = Sin A. Cos A$ and x.sin A = y.cos A show that

$x^2 + y^2 = 1$.

Q 4. If cos A / Cos B = m , Cos A / Sin B =  n show that

$(m^2 + n^2 ) cos^2 B = n^2$

Q 5. If tan A + Sin A = m  and tan A – sin A = n prove that

$(m^2 -n^2)^2 = 16 mn$

Q 6. If cosec A + cot A = p , prove that $(p^2 + 1)cos A = p^2 - 1$

Q 7. Find the value of the other trigonometric ratios if cos A = $2 m/ (m^2 +1)$

Q 8. If tan A = p/q , show that

$(p sin A - q cos A) / (p sin A + q cos A) = (p^2 - q^2 )/ (p^2 + q ^2)$

Q 9. If tan B = a/b , find the value of

( a Sin B + b cos B)/ (a sin B – b cos B)

Q 10. if $x = a. cos^3 A , y = b. sin ^3 A$

Prove that  $[ x / a ]^2/3 + [ y/b ]^2/3 = 1$

Note : Ensure methods to be written clearly. Marks given for method shown also.

## Oh ! the loud voices

I hate my parents when they give me advice,

Especially when they do it more

Than thrice.

I get it , I get it

I get the point

Now I know more than

My favorite food joint

The advice comes in like swords

Of fire.

You aren’t  liar

I don’t want their voice

To go higher,

Silence right now

Is only the thing I  desire.

But they will never stop,

The day will never come,

A perfect human they want

You to become

Then you realize your

The advice is not to make

Eyes drool

No, not to make you look like

A fool .

Its because they have love

For thee

A perfect human they want you to be.

Written by

Ashwin

Drawings by

The smile

There is a Smile,

Just a far a mile

I  want  to try ,

So that  I  can help

The people who cry

That to make our nation

More clean and  more beautiful

Smile should  be

Anywhere and  everywhere

Do your  Best to get

A  best  smile in your

Lovely face.

Written by

Ritika Singh

Class V

Euroschool.

## How to utilize your summer vacation to maximum.

Summer vacation is around the corner for all school students from CBSE , ICSE and state board.  Generally if somebody doesn’t plan that itself is plan  which gets executed without you knowing it. So its better to know the plan before and execute it later than its instant execution without aware of planning . So here we list down some of the best plans students can decide to do this summer and after vacation they are looking forward for the next best future learning

1. Make habit of getting up early in morning by 7 am or before. Utilize 1 hour time for your body exercise. It can be anything which person likes. May be playing their favorite games also.

2. Make sure you learn something new this summer apart from what you learnt in school. This can happen only when you know what you want to learn It can be something new. Like new programming language C++ or java . Python,    Or cooking / singing /drawing/ painting / drama / dancing / if you haven’t been public speaker practice extempore and do public speaking .

3. Play your outdoor games hard. Every day make sure you play your sports.

4. Learn 1 song every week. It doesn’t mean you need to do singing. If you like singing well its great. If not still remember it , it challenges your mind to know something new.

5. Talk to your parents for 30 mins every day.

6, Eat food prepared by mom every day at home. During these holidays no goals should be made for eating junk food.

7. Have fruits at night most of the time after dinner.

8. Play online game fortnite only for 1 hour. It might be difficult but yes its needs to be time bound else it will eat whole day.

9. Challenge yourself to read  15 min your favorite book every night.

10. Make sure you study for 1 hour your school text books and it must be productive. Its difficult but can be manageable once you put mind and soul in it.

Wish you wonderful summer holidays and Have fun 🙂

Who has to develop reading habit ?
Why some body has to read books ?
Am done with reading all kinds of books why I should read books?
When we are in the childhood days we learn everyday new things by going to school, learning something new each day and discussing with parents and this is driven by automatic process.
Our mind enables us to learn new words , new ideas , new topics and new ways to work.
As when education gets completed, do people have the habit of reading , I suppose no
unless some body is in the professional field where you need to learn new programming language new project etc.
the problem with the grown ups is that they don’t read at all. They are in the complacent zone.
They have studied every thing they don’t need to know any further.

It seems like soil saying I don’t need to be fertile any more I have already grown paddy and wheat in my field.
When nothing is grown on the land , what automatically grows it just weeds. Natures law of proving every time. When soil is not utilized continuously for crop rotation and left barren for long time, it attracts
growth of weeds automatically.

We are all humans. Many times we have come across very creative ideas when we are shifted to all together different thing after being busy in same routine work. New idea emerges when we read books. How to develop habit of reading books right from childhood. Today in the current scenario there is no limit to how much you can see youtube , online movies, all www. so on.. Even 24hrs is too less to browse through the information which is available online and watching TV. How to induce habit of reading books ?There is no hard work in doing this, lets start with 15 mins of reading daily. which book to pick up ? let parents decide for the children. It can be story book, animation, fiction , non fiction, mythology etc.. Once habit of reading is cultivated in the children at the formative stage. It brings out lot of creative skills to them. They communicate new ideas. show respect, mingle well and do good in studies sports extra curricular activities. They start thinking in terms of doing something which they like to do and how they can excel and bring about wonderful change in the them, and hence happy home to wonderful society to awesome state to great country.

Thanks

www.Tuitionrocks.com

## Going eXtra Mile

Some body’s goal is to get cent percent marks in board exam. One wants to be best player in badminton. One wants to be best in athletics. One wants to be best in swimming. One wants to be best employee. One wants to be best sculpturist. So there are enough example where we see one wants to do the best in the designated field or goal which they have set.
So why some body doesn’t get what
they want to be even after putting the effort.

Here I am not talking about going from good to better. That’s easy and 99% of people achieve it when they have will do to what is required. What’s more important is going from better to best, good to great , better to excellence, silence to tranquility. How come very few or 1% only can achieve it. What’s missing point?.

Going eXtra mile is all about you do things one more time when you are tired. When you feel like not doing something but still do bcoz that’s right for you. When somebody wants to do body building he does one more set of push-ups even when he got tired.
When some body wants to do one more round of running race even his time is over.
When some body wants to be best employee he takes up one more extra assignment when his targets are over.

There is great set of differences present when one wants to achieve 100% marks in any subject and one one who wants to go beyond 100%.
How a person who already scores range of 95-96 marks all the time to make them reach beyond 100%.

That’s where excellence comes in picture. One sculpture made two statues exactly similar. One customer comes and ask for one to buy. But Sculpture says Sir this one is sold out but other one I can’t give as it has minor defects in its nose and ear. Customer hardly notices those minor defects. For him both looked exactly similar. It’s act of excellence which sculpture shows that even there is similarities in some body’s else eyes but not in the eyes of professionals.

So in order to achieve 100% in any of your Goals you just need to think beyond 100%.
One of our students who scored more than 100% in her thinking by going beyond 100% and achieve the target which she had set for herself with great sense of achievement and satisfaction.

Thanks

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## Class IX to XII. How to attempt in limited…

Many time it happens for the students of grade IX to XII that they know the concepts and when they start writing the exam doubt becomes their strange friend and tend to do the mistakes which is less known to them.

And most of the time it arises that the same questions which they had done earlier, they end up without solving it and so much energy and time wasted.

Do they don’t know the method of how to write the exams , you bet ?. They know each and every thing in the theoretical ways and can guide new comer about how to write exams in most effective way.

what happened then?

There is big difference in the mindset which they carry in one in which time is bounded in certain limits. And other when there is no time-bound.

Remember when any body does the practice match lets say football, cycling or swimming, they just enjoy and finish learning without even worrying of what happened. There is no pressure for finishing early, There is no pressure even they make mistakes in learning , there is no hurry to show to anyone your results of the match, All together no one is there to judge you about your attempts and how you played.

And suddenly the things changes when doctor asks the patient that you have only 1/2 year to survive you are allowed to live life to the fullest in limited time. What do you think patient gonna comprehend in his mind. The things which he has not thought till now , he starts thinking in that direction. Does he wants to do certain things which he had wished and procrastinated? Of-course YES. Does his new mind-set developed over the existing mindset?

Ans is Yes.

What happens to the students when they start the test or exam in the time limited way?

1. They carry all together different mind-set.
2. They start thinking about the topics which they are weak in and have not practiced thoroughly.
3. They develop the pressure what if they not able to finish in time.
4. What if they fail in the exam.
5. What if they not perform well in the exam. How they will withstand their parents.
6. Activity in the brain lets all the self-induced thoughts vibrate about their mean position.
7. Immediately Brain starts to think about the formulas which they haven’t remembered.
8. On the top of this when they see time during the test , their vibrations of thought Time period is reduced.

How we have been handling the above issues all the time? They have been doing consistent practice in the limited time bound approach every time when they finish one Chapter or Subjects anything. And measure all the time the progress with the previous time. Are you improving by measuring how were you yesterday to how are you today ?

Thanks

## How to know your child needs Tuition

This becomes general question in the mind of parents which exists as the hidden agenda. when not given the priority it just fades away else they discuss with friends and relatives which is the best place for sending students for extra studies.

As a parent when they realize that their child requires extra education apart from the regular School education?

Thanks to our education system in India which tells us where our child stands in the grading system or marks system what ever be the case and notified in the PTM(Parents Teachers Meeting/Communication).

Now it triggers in Parents to search for the particular Tuition place or home Tuition to get their child maximum score in the subjects chosen.

Do the Assessment from School is only factor to know that your child needs extra Tuition ?

And your Child wants to score 100% in all the subjects defined by Parents as in the Class every body has to be on the top.

Answer to the above question is NO….

If you can answer the below questions true to your knowledge , then it may sound your ward needs attention.

1. Do you spend quality time with your kid? Discussing the issues faced by them in the subjects mentioned.
2. Do you know that he/she wants to do better in certain sports?
3. Do you know if they really know which subjects they are good in and which they are weak in ? not based on the academic results.
4. Do you know how much time child devotes in the today’s gadgets like mobile / ipad etc?
5. Have you ever sat any time to praise what they are good in and encourage mostly in their Strength area ?
6. Did you ever sit with your child as friend and do his homework together?
7. Is there an openness environment created in the home which can tell child freely about his interest areas ?
8. If Both parents are working do the child gets most attention by Maids or care takers at home?
9. Does your child tells what interesting things he/she learnt at School every day  ?
10. Today 1 out of 3 child is pursuing more than 3 extra curricular activities along with their studies , it can be Art, Western Dance , Classical Dance , Football, Basketball , Guitar , Swimming, Cricket , Karate  etc. Is he/She is clear what they want to do ?

Children are busier than parents. So it is reverse attention. Children give time to parents rather than Parents giving time to Children.

So please pay attention at the beginning  Gone are the days when the very first criteria was assessment from school to go for tuition. Today Tuition is viewed as mentor ship program to enhance kids strength area , look forward with better visibility and to be happy in his life.

Children are there at home for just 10 years. After that they fly away and live their own life. In the blink of eye 10 years will pass. As a Parents Least you can provide is the right education with great Mentor ship Program.

Thanks

## Embracing Online Tuition

When was the last time you took a picture from your Digital Camera? When was the last time you waited for your turn to call from landline phone? When was the last time you bought smart phone from Shop? When was the last time you bought grocery from Kirana shop? When was the last time you bought movie tickets from counter? When was the last time you waited at Bus stop and waved for hiring Taxi ? We are currently living in the fast paced changing technology environment.

Now it makes people to think how to go back in just recent past to know what they were using so-called digital camera to take every snap for every occasion. Now those cameras are only used by professional photographers. Thanks to the smart phone now people don’t have to carry exclusive camera to take pics. Now hardly people make call from Landline , its decorative piece of souvenir now in home. Either you go to Mall or Mall comes to your home for grocery . You book tickets online and show bar code. You don’t wait for the going to near by stand for hiring taxi, you use App instead to book and taxi comes near you.

Did we embrace changes very fast ? yes we did .

Earlier we used to have so many Tuition at home. Now since in the fast changing world, everything needs to be instant. Lets look at the feasibility for the home Tuition in the city of Bangalore. Do people are worried about the traffic ? yes of-course . here we count the distance in terms of time. Suppose person has to go from silk board to Whitefield, it will take 3 hrs in busy traffic . and going back same . Its lil bit exaggerated but the point is you end up wasting time in totally unproductive work. Today many companies offer work from home options. Earlier comforts are today’s needs.

From home tuition to online home tuition the shift is in the mindset rather than keeping the old sentiments of having doubt clarification in person.

Today hundreds of tutorials exists in the online space. People have a problem of Abundance not the  Problem of Scarcity.

You want to learn about any topics just type in you tube and you are on it . The convenience is such that its been exploited so much. The shift has taken place.

Today we conduct online Tuition, what we have figured out is this.  In US, UK Australia and Singapore its common. In India we take time to embrace and hence we become top market in the world , Its simple

1. Credibility is built through face to face meeting.
2. Reference do work as trust can be established only when person you know in person recommends other.
3. Time Respect is indeed mandatory.
4. Agenda needs to be very clear for online Tuition, what subject to be taught and when the doubts needs to be clarified.
5. Everybody is having WiFi at home.
6. Quality for this Teaching will be higher , as this involves available resources.
7. Evaluation can be done offline when person sends the screen shot of his Answer sheets using smart phone.

Thanks,

## Goal Driven Tuition

Hello All,

Have you ever seen when kids play their favorite games they set their own goals believing that they can achieve it and play hard to surpass it. Whether it is Basketball , Cricket , Volleyball, Skating, Cycling, Badminton etc. Kids at the young age have full of excitement , energy and zeal to achieve the target set by themselves.

The whole process of believing it with heart and setting their own goals and enjoying the game which they like to play is called Goal driven Games. Have not seen any kid  ( esp age group 10-17) when playing in group or playing

by themselves without competing with each other and don’t want to improve the game for their advantage.

The guy who is good in Bowling in Cricket , he wants to take more wicket than the previous time another guy who is playing Basketball wants to put 1 extra basket every other time , Guy playing Skating wants to put his heart to do nice moves and tricks every other time , Guy who is cycling wants to finish the cycling in lesser time compared to last time and the guy who loves badminton wants to win the match every time with his opponents.

What I am trying to prove is natural way Young minds understand the process of goal setting and working towards it innocently. That’s the nature’s law of growth in any phase of life. Happiness is the progressive realization of worthwhile goals.

Coming to the Tuition, When we set the goals for the them in Studies which becomes their primary activities in the life and they believe it with their heart and work in the same zeal you don’t need to micromanage them. They will show the results in appropriate time. They just need only guidance and friend who is by side with them. We have similar examples coming all the time. Every Student has set his own goals and working towards achieving it. And he/she has a lot of fun in the journey.

Thanks