rewrite the expression in terms of the first power of the cosine.

Question

sin^8x

Answer 1

Recall that sin^2(x) = 1/2 (1-cosx)

use that several times to end up with

sin^4x = 1/8 (cos4x - 4cos2x + 3)
and on to
1/256 (cos8x - 8cos6x +28cos4x - 56cos2x + 35