Question

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

Answer 1

Prove trig expression P

Explanation:

The expression in the parentheses can be transformed to:
`(1 - 2cos^2 x + cos ^4 x) = (1 - cos ^2 x)^2 = (sin^2 x)^2 =`
`= sin^4 x.`
Therefor the product becomes -->

`P = sin x(sin^4 x) = sin^5 x`