Question

Express the quantity sin^6(x) in a form that does not involve powers of trigonometric functions.

Answer 1

Make use of the double angle formula for cos:\[\cos(2x)=1-2\sin^2(x)\]If you rearrange this you will get:\[\sin^2(x)=\frac{1-\cos(2x)}{2}\]

Answer 2

Use this and you will end up with the desired answer

Answer 3

additional hint:
similarly \(\large \cos^2(x)=\frac{1+\cos(2x)}{2}\)