# How can I simplify sin2xcosx+cos2xsinx?

Use the identities: $\sin 2 x = 2 \sin x . \cos x$ and
$\cos 2 x = 2 {\cos}^{2} x - 1$
$2 \sin x . {\cos}^{2} x + \left(2 {\cos}^{2} x - 1\right) \sin x$=
$= \sin x \left(4 {\cos}^{2} x - 1\right) = \sin x . \left(2 \cos x - 1\right) \left(2 \cos x + 1\right)$