Question

I have no idea how to do this one. ​

Answer 1

use (1 -cos²x) for sin²x and expand

Explanation:

You want to verify sin⁴x·cos²x = cos²x -2cos⁴x +cos⁶x.

Pythagorean identity

You can get the desired result by substituting (1 -cos²x) for sin²x.

`\sin^4{x}\,\cos^2{x}=(1-\cos^2{x})^2\,\cos^2{x}=(1-2\cos^2{x}+\cos^4{x})\cos^2{x}\\\\=\boxed{\cos^2{x}-2\cos^4{x}+\cos^6{x}}`