Simplify sin x cos^2 x − sin x

Question

Please help.

Answer 1

First factor out a common monomial factor and than use a fundamental identity.

       sin x cos² x − sin x = sin x(cos² x − 1)            Factor out common monomial factor.

                                       = − sin x(1− cos² x)          Factor out − 1

                                       = − sin x(sin² x)                 Pythagorean identity

                                       =− sin³ x                             Multiply