Question

How can I simplify sin2xcosx+cos2xsinx?

Answer 1

Use the identities: `sin 2x = 2sin x.cos x` and

`cos 2x = 2cos^2 x - 1`

`2sin x.cos^2 x + (2cos^2 x - 1)sin x`=

`=sin x(4cos^2 x - 1) = sin x.(2cos x - 1)(2cos x + 1)`