Question

How do you prove `1+ sin(x)= 2*cos^2 (pi/4- x/2)`?

Answer 1

Please see below.

Explanation:

`cos(pi/2-x)=sinx`

Now `cos(pi/2-x)=cos2(pi/4-x/2)`, hence

`sinx=2cos^2(pi/4-x/2)-1`

or `1+sinx=2cos^2(pi/4-x/2)`