Question

Use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine.

(sin^6(x))

Answer 1

First of all,
cos(2x) = cos^2 x - sin^2 x
= 1 - 2sin^2 x
=> sin^2 x = (1/2)(1 - cos(2x))

Thus
sin^6 x = 1/8(1-cos(2x))^3

Now expand that and reduce the terms in cos^2 x and cos^3 x