Answer:
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
