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

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

sin x * sin x = 1/2 (cos (x-x) - cos (x+x)) = 1/2 (cos (0) - cos (2x))

Step-by-step explanation:

sin² x = sin x * sin x

using the product-to-sum identity for sine

sin x * sin x = 1/2 (cos (x-x) - cos (x+x)) = 1/2 (cos (0) - cos (2x))

cos (0) = 1

sin² x =  (1 - cos (2x)) /2

by definition, an arc subtended by a central angle of some given measure has the same measure. so .