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

Question

How do you verify the identity?

Answer 1

sin⁵xcos²x = sinx(sin⁴x)cos²x = sinx(sin²x)²cos²x

 

                                          = sinx(1-cos²x)²cos²x

 

                                          = sinx(1 - 2cos²x + cos⁴x)cos²x

 

                                          = sinx(cos²x - 2cos⁴x + cos⁶x)

Answer 2

sin^5xcos^2 ⇐ First, fix the missing argument for the squared cosine factor on the left side.

 

This looks extremely tedious. I'd work with the left side, factoring out sin x, and do substitution of sin⁴x  by (1-cos²x)² as starters. Good luck.