Rewrite sin(x)cos2(x) − sin(x) as an expression containing a single term

  -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