Prove this identity using the product-to-sum identity for sin ... sin^2 x = (1-cos (2x)) / (2)

sin²x = (1 - cos2x) / 2 ⇒ proved down

Step-by-step explanation:

∵ sin²x = (sinx) (sinx) ⇒ add and subtract (cosx) (cosx)

(sinx) (sinx) + (cosx) (cosx) - (cosx) (cosx)

∵ (cosx) (cosx) - (sinx) (sinx) = cos (x + x) = cos2x

∴ - cos2x + cos²x = - cos2x + (1 - sin²x)

∴ 1 - cos2x - sin²x = (1 - cos2x) / 2 ⇒ equality of the two sides

∴ (1 - cos2x) - 1/2 (1 - cos2x) = sin²x

∴ 1/2 (1 - cos2x) = sin²x

∴ sin²x = (1 - cos2x) / 2