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Trigonometric Ratios Of Compound Angles — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Ratios Of Compound Angles3 Marks
Question
Prove that:
$\sin4\text{x}=4\sin\text{x}\cos^3\text{x}-4\cos\text{x}\sin^3\text{x}$
✓

Answer

$\text{LHS}=\sin4\text{x}$
$=\sin2.2\text{x}$
$=2\sin2\text{x}\cos2\text{x}$
$=2(\sin\text{x}\cos\text{x}).(\cos^2\text{x}-\sin^2\text{x})$
$=4\sin\text{x}\cos^3\text{x}-4\sin^3\text{x}\cos\text{x}=\text{RHS}$

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