Question

Why sin x is written as 2sinx/2 cost/2 and 1+cosx as 2cos sq x/2

Answer 1

Answer:

Step-by-step explanation:

There is a concept of double and half angles which is taught when you go in 11th.

The double angles state that

Sin2x = 2CosxSinx

now half angle states

Sinx = 2Cosx/2Sinx/2

and double angle of cos is

Cos2x = cos²x - sin²x

or

2cos²x - 1

or

1 - 2Sin²x

now if you apply the same thing as we did before

cosx = 2cos²x/2 - 1

which is Cosx + 1 = 2Cos²x/2

Hope this helps ☺️

If you want to know the derivations, please comment on this Answer and I will edit this answer with derivation and explanation ☺️