trig questions

which of the following is equivalent to the expression sin 2x cos x-sin x cos2x 

a. sinx

b. sin 3x

c. cos x

d. cos 3x

Hello Debnath!

\(sin 2x\ cos x-sin x\ cos2x\\ = 2\ sinx\ cosx\ cosx-sinx\ (cos^2x-sin^2x)\\ =2sinx\ cos^2x-sinx\ cos^2x+sin^3x\\ =sinx\ cos^2x+sin^3x\\ =sinx(cos^2x+sin^2x)\\ =sinx\ \cdot 1\)

\(sin 2x\ cos x-sin x\ cos2x=sinx\)

  !