Question

Proove:
a) 1+sinx=(sin(x/2)+cos(x/2))²

b) sin(x+π)+sin(x-π)=-2sinx

c) cosx+cos(x+120°)+cos(x+240°)=0

I tried to proove all of these but I always got something weird that I don't understand.

Answer 1

Can you show how you tried?? Let us start with first one..

Answer 2

You write, may be it is the case, that your approach is good, but you are doing one or two mistake in between which we will correct, so, don't worry about mistakes, just tell me how you started the first one?

Answer 3

okay, just wait a minute i'll find if in my notes

Answer 4

*it

Answer 5

Sure, take your time.. We are in no hurry.. :)

Answer 6

1+sinx=(sin(x/2)+cos(x/2))²
1+sinx=sin²(x/2)+2sin(x/2)cos(x/2)+cos²(x/2)
1+sinx=sin(x/2)sin(x/2)+2sin(x/2)cos(x/2)+cos(x/2)cos(x/2)

Answer 7

thats all I was able to do with it.

Answer 8

You are just close to it..

Answer 9

Basically you need to know three formulae here to do this problem, one you know, other two I will tell you.. :)

Answer 10

\[1. \quad \sin^2(a) + \cos^2(a) = 1\]
\[2. \quad 2\sin(a) \cdot \cos(a) = \sin(2a)\]

Answer 11

you are good up to your second step..

Answer 12

I mean no need to go for third step..

Answer 13

Can you try to use that formulae in second step or need help?

Answer 14

\[\sin^2(\frac{x}{2}) + \cos^2(\frac{x}{2}) + 2 \sin(\frac{x}{2}) \cos(\frac{x}{2})\]

Answer 15

i'll try it

Answer 16

Okay, you must try yourself, you will be benefited more.. :) And any doubt or any problem anywhere, let me know.. :)

Answer 17

1+sinx=(sin(x/2)+cos(x/2))²
1+sinx=sin²(x/2)+2sin(x/2)cos(x/2)+cos²(x/2)
1+sinx=sin²(x/2)+cos²(x/2)+2sin(x/2)cos(x/2)

sin²(x/2)+cos²(x/2)=1
2sin(x/2)cos(x/2)=sinx

1+sinx=1+sinx

Answer 18

Oh wow.. :)

Answer 19

But, you need to know how to represent your proof nicely.. :)

Answer 20

You are writing Right Hand Side (RHS) and Left Hand Side(LHS) altogether, Take one side at the time, prove it equal to other side.. :)

Answer 21

Getting me??

Answer 22

well, teacher at elementary school told us that we just have to write this: left=right

Answer 23

Really?

Answer 24

If you want to know, then I can tell.. :)

Answer 25

Show him how to do it Water...

Answer 26

Okay Ma'am.. :)

Answer 27

i was just trying to get throught the language barrier, sorry :D

Answer 28

You should take any one of the side, like you are doing it for RHS then you will do like this: