simplify the given expression

Question

cos ( 2x ) sin( x ) - sin ( 2x ) cos ( x )

Answer 1

cos(2x) sin(x) - 2 sin(x)cos(x) cos(x) =

cos(2x) sin(x) - 2 sin(x) cos^2(x) =

(2 cos^2(x) - 1)(sinx) - 2 sin(x) cos^2(x) =

2 cos^2(x) sin(x) - sin (x) - 2 cos^2(x) sin(x) =

= - sin(x)