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Trigonometric Ratios Of Compounds — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Ratios Of Compounds3 Marks
Question
Prove that: $\cos4\text{x}-\cos4\alpha=8(\cos\text{x}-\cos\alpha)(\cos\text{x}+\cos\alpha)\$\cos\text{x}+\sin\alpha)(\cos\text{x}-\sin\alpha)$
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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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