sin a. cos^(3)a - cos a.sin^(3)a

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Solution

Dear student
$\sin a \cos^{3} a - \cos a \sin^{3} a = \sin a \cos a (\cos^{2} a - \sin^{2} a) = \sin a \cos a (\cos 2 a) [∵ c o s^{2} x - s i n^{2} x = \cos 2 x] = \frac{1}{2} \sin 2 a \cos 2 a [∵ \sin 2 x = 2 \sin x \cos x] = \frac{1}{4} \sin 4 a$
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