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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:
$\cos4\text{x}-\cos4\alpha=8(\cos\text{x}-\cos\alpha)(\cos\text{x}+\cos\alpha)\$\cos\text{x}+\sin\alpha)(\cos\text{x}-\sin\alpha)$
✓

Answer

$\cos4\text{x}-\cos4\alpha=2\cos^22\theta-2\cos^22\alpha$
$=2(\cos2\text{x}+\cos2\alpha)(\cos2\text{x}-\cos2\alpha)$
$=2(2\cos^2\text{x}-1+1-2\sin^2\alpha)(2\cos^2\text{x}-1-2\cos^2\alpha+1)$
$=8(\cos^2\text{x}-\sin^2\alpha)(\cos^2\text{x}-\cos^2\alpha)$
$=8(\cos\text{x}-\sin\alpha)(\cos\text{x}+\sin\alpha)(\cos\text{x}-\cos\alpha)$

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