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Trigonometric Functions — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Functions2 Marks
Question
Prove that $4\text{A}=4\sin\text{A}\cos^3\text{A}-4\cos\text{A}\sin^3\text{A}.$
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Answer

$\text{L.H.S.}=\sin4\text{A}$
$=2\sin2\text{A}-\cos2\text{A}=2(2\sin\text{A}\cos\text{A})(\cos^2\text{A}-\sin^2\text{A})$
$=4\sin\text{A}.\cos^3\text{A}-4\cos\text{A}\sin^3\text{A}=\text{R.H.S.}$

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