Question

How do you verify `sin^5xcos^2x=(cos^2x-2cos^4x+cos^6x)sinx`?

Answer 1

See below

Explanation:

Operating in both sides

`sin^5xcos^2x=(cos^2x-2cos^4x+cos^6x)sinx`
`sin xsin^4xcos^2x=(cos^2x-2cos^4x+cos^6x)sin x`
`sin xsin^4xcos^2x=(1-2cos^2x+cos^4x)cos^2x sin x`
`sin xsin^4xcos^2x=(1-cos^2x)^2cos^2x sin x`
`sin xsin^4xcos^2x=sin^4xcos^2x sin x`