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How can I simplify sin2xcosx+cos2xsinx?

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May 28, 2015

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

$cos 2 x = 2 {cos}^{2} x - 1$ $cos 2x = 2cos^2 x - 1$

$2 sin x . {cos}^{2} x + (2 {cos}^{2} x - 1) sin x$ $2sin x.cos^2 x + (2cos^2 x - 1)sin x$ =

$= sin x (4 {cos}^{2} x - 1) = sin x . (2 cos x - 1) (2 cos x + 1)$ $=sin x(4cos^2 x - 1) = sin x.(2cos x - 1)(2cos x + 1)$

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