Question

alright. here we go. a long one.
verify : sin^5xcos^2x = (cos^2x-2cos^4x+cos^6x)sinx

Answer 1

Turn all but one of the sines into cosines using the pythagorean identity and then multiply it out.

\[\sin^{2}x + \cos^{2}x = 1\]
\[\sin^{2}x = 1-\cos^{2}x\]

Answer 2

Mmm.. do i factor anything out first?

Answer 3

Well, you first rewrite it like this:

\[\sin^{2}x = 1-\cos^{2}x \implies \sin^{5}xcos^{2}x= sinx(1-\cos^{2}x)^{2}(\cos^{2}x)\]Just dont multiply in that sinx, keep it out. If you only multiply out the cosines you should have it.

Answer 4

alright, thanks!

Answer 5

Yep, np ^_^