Answer: -2sin³x
Step-by-step explanation:
cos ( x + y ) = cosx*cosy - sin y*sinx (1)
if x = y (1) could be express as: cos (2x) = cosx*cosx -sinx*sinx
cos 2x = cos²x -sin²x
Then sin(x)*cos2(x) − sin(x) ⇒ sinx * ( cos²x - sin²x ) - sinx
multiplying sinx*cos²x -sin³x -sinx
sinx (commom factor sinx (cos²x -sin²x -1) but 1-cos²x = sin²x
or -1 +cos²x = -sin²x ⇒sinx( -sin²x -sin²x) ⇒sinx (-2sin²x)
-2sin³x
