Given sin 2x cos 3x sin 2x ( cos( 2x+x ) #160; #160; ) =sin 2x ( cos 2x cos x sin 2x sin x #160; ) =sin 2x cos 2x cos x sin ^ 2 ...

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Trigonometric Identities

Solve sin 2...

Question

Solve $sin 2 x cos 3 x$

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Solution

Given $sin 2 x cos 3 x$
$sin 2 x (cos (2 x + x))$
$= sin 2 x (cos 2 x cos x - sin 2 x sin x)$
$= sin 2 x cos 2 x cos x - {sin}^{2} 2 x sin x$
$= 2 sin x cos x cos 2 x cos x - 4 {sin}^{2} x {cos}^{2} x sin x$
$= 2 sin x cos 2 x {cos}^{2} x - 4 {sin}^{3} x {cos}^{2} x$

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