Question

Write the trigonometric expression as a sum or difference
3sin2xsin3x

Answer 1

sin3x=sin(2x+x)=sin2x.cosx+cos2x.sinx

=2.sinx.cos^2x+(cos^2x-sin^2x).sinx

=3.sinx.cos^2x-sin^3x

=3.sinx(1-sin^2x)-sin^3x

=3.sinx-3.sin^3x-sin^3x

=3.sinx-4.sin^3x

i.e. sin3x=3.sinx-4. sin^3x. ....eq.(1)

& sin2x=2.sinx.cosx. .....eq.(2)

therefore ,

3.sin2x.sin3x=3.2.sinx.cosx(3.sinx-4.sin^3x)

3.sin2x.sin3x=18.sin^2x. cosx-24.sin^3x.