Question

Question #fa425

Answer 1

Please look below

Explanation:

Lets start with RHS;

`(1 + cosx)/ 2 = (1 + cos(2 * x/2))/ 2 = (1 + cos^2 (x/2) - sin^2 (x/2))/2`

`= ( cos^2 (x/2) +sin^2 (x/2) + cos^2 (x/2) - sin^2 (x/2))/2`
`= ( cos^2 (x/2) +cancel(sin^2 (x/2)) + cos^2 (x/2) cancel(- sin^2 (x/2)))/2`

`=( cancel(2)cos^2(x/2))/cancel2 = cos^2 (x/2) = LHS`

Hence Verified