NEED ASAP! write 6sin^4 (x) in terms of first powers of cosine

Question

WRITE: 6sin⁴(x)

in terms of first powers of cosine

Answer 1

From the reducing power identity (sin^2 x) = (1-cos2x)/2

so 6(sin^2)^2 = [(1 - cos2x)/2]^2 = (1 -2cos2x +cos^2)/4

from reducing power identity for cos^2 = (1+cos2x)/2

So {1- 2cos2x + [(1+cos2x)/2]}/4

Simplify and you will get (3-3cos2x)/8