Question

How do you prove `sinx(1-2cos^2x+cos^4x)=sin^5x`?

Answer 1

Prove trig expression.

Explanation:

The quantity i the parentheses -->
`(1 - 2cos^2 x + cos^4 x) = (1 - cos^2 x)^2 = (sin^2x)^2`. Therefor
`sin x(1 - cos^2 x + cos^4 x) = sin x.sin^4 x = sin^5 x`