Prove this identity using the product-to-sum identity for sine:

Question

sin^2 x=1-cos(2x)/2

Answer 1

YOU MEAN
sin^2 x=[ 1-cos(2x) ] /2
or
2 sin^2 x = 1 - cos(2x)

cos 2 x = cos^2 x - sin^2 x

so
2 sin^2 x = 1 - cos^2 x + sin^2 x

sin^2 x = 1 - cos^2 x
or
sin^2 x + cos^2 x = 1
which is true