## 7 Important life lessons everyone can imbibe today :

1. Dreams :  Dream is the starting point for all your living. We humans are different from animal world in big way because its us who have ability to dream. Why are you living? What do you want to achieve? Dream can be defined at every level.People should realize the potential of dream at the very early age.I came across the dream concept only when I joined the job after finishing my college engineering. Little did I know that I was all the time pursuing the goals one at a time. Dreams can be different  at different level.When you are student parents sets goals for you.When you are working , your boss sets goals and dreams for you.Everybody has dreams. Whats more important is whether its crystal clear in written form or not. Personalized dreams is very important in life. Its so easy to get diverted with the information overload.Personalized Dreams is very important which fuels your passion to lead your life.After working for last 16 years I realized that I need to pursue my dream in the area which I like. Today I am living my dream of imparting knowledge to young minds. I work with my own defined timings and targets and it doesn’t feel like working when you love to do what you  enjoy and at the same time you have peace of mind and you don’t have any guilt.

2. Health :  Exercise is must at all the age. Its defined by individual and who wants to do things which they love to do. To keep your body healthy , it also requires maintenance. To share your emotions , thoughts , happiness , sorrows. ideas and to have fun and entertainment you need friends and families. Every day do some thing to be connected with these folks in your life. They are there through out for your life. Take care for them reward them with surprises, Living person must be rewarded more every day than dead person. Laugh a lot, entertain yourself, rejoice and live to the fullest. Its must. Balancing is the key. You must be connected to your spiritual level by doing meditation or sitting quietly for some time.Giving personal time to yourself. In a quiet mind. You talk to yourself. Self perpetual process. Exercise that increase your Adrenalin level will help through out the day. You are not lazy any more.

3. Finances : When people starts working and get busy in making money. What happens to their lifestyle. They want more and when people starts working and get busy in making money. What happens to their lifestyle. They want more and more.. Person who has 99 wants 100. This is good. Here there may be certain factors which come into play  like people make x amount of income and x+1 goes out. Charity begins at home. We have enough number of times this proverb. How this is different than others. Look at the simple division of finances for balanced living when person makes \$100 income. He has to keep 10\$ for the charity. And rest 40\$ for expenses and rest 40\$ for saving and remaining 10\$ for miscellaneous which comes up unknowingly. So person at any level making any amount of income can do this planning for successful living. Look at the phenomenon example of all the millionaires and billionaires who are leading the balanced life, they all have charitable trust. Its only when your hunger is satisfied, you can fulfill wishes of others. 5 Areas which must be in balanced condition. example.Finances, Spiritual, Mind, body, friends and Family. When you are healthy , you love to do  all the things and body is free to do. When you are economically healthy, you are at peace and can take decisions well. Only healthy body can do persistence and consistence exercise. Same way Economically healthy person can invest appropriately.

4. Accountability :  This word is less known to us. May be this word is key word only for the Bank and commerce field.
It just refers to certain aspect of individual character. What it means you talk the walk and walk the talk.
Its word given to somebody which can’t be taken back. If you promise to deliver your work , your time,
your deliverables on certain date and time Are you meeting those criteria put up by you. Its the self
realization goal. When you are your own Boss you realize more of accountability as your commitment matters
lot to many of your clients and making each and every customer a delightful customer.

5. Learning : Learning doesn’t define any age.You can pick up any book and just develop the habit of reading 10-15 mins daily for mind. New ideas is worth getting you excited for the future life. Have read wonderful book named ” The power of Subconscious Mind” by Author Joseph Murphy. He says every day people generate close to 40-50k ideas. That’s a good thing and bad thing is that it gets repeated every day. Arjun was best student for Krishna. Arjun was always in learning mode from Krishna. Who is being known through out the world. Simple analogy is to understand and learn the area which you are working, studying, or doing business. Dynamics of this world is changing every day. You must change as per the need for the world.
new solutions to new challenges. We must align and think continuously in this direction.

6. Association :  You select better association as per your dreams. When you are working as employee, you will think like an employee    You select better association as per your dreams. When you are working as employee, you will think like an employee  When you are with entrepreneurs you will think like them. When you are more with religious people , your brain also will start thinking religiously. When you are with sportsperson, you will start to think in terms of winning  the game. When you are with politicians , you automatically start to think all the time to win the elections. Simple analogy is to decide what kind of association you want. To get some things you have to leave some things. Some people comes in your life to be your friends. Some people comes to give you only advice. Some people will challenge you to do better of you always. Few people will try to put you down. So all are the choices available to us.

7. Entertainment: Never be workaholic. Enjoy the work which you love to do. People will say you are workaholic. People will say you are workaholic. When you ask any workaholic person is he workaholic he will say no. so where does this perception comes. Its in the others eyes. Every body does best in the field which they love to do. There is no restriction for the what kind of entertainment you want, food and drinks you want. The reason being said in accordance with the exception of having great entertainment we must strive to have entertainment in the life, Keep your romance alive all the time. Go out for dinner, lunch or vacation different city , having coffee, beers and wines with your friends.Hang out with your friends and have fun. It blessing to have good friends in your life. Do light up your personality to bring great vibes in life and pass to the society. Happiness is contagious.

Thanks

Ranjit Singh

## 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 🙂