Rewrite as an expression that does not contain trigonometric function of power greater than one.

Question

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

Rewrite as an expression that does not contain trigonometric function of power greater than one.

Answer 1

sin(2θ) = 2sinθcosθ

So, sin(x/2)cos(x/2) = (1/2)sinx

1 - 2sin²θ = cos(2θ)

So, 1 - 2sin²(x/2) = cosx

Therefore, sin(x/2)cos(x/2)(1 - 2sin²(x/2)) = (1/2)sinxcosx = (1/4)sin(2x)

Answer 2

Use:

sin² x = (1 - cos 2x) / 2