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Trigonometric Ratios Of Compounds — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Ratios Of Compounds2 Marks
Question
Prove that: $\sqrt{2+\sqrt{2+2\cos4\text{x}}}=2\cos\text{x},0\cos\text{x},<\text{x}<\frac{\pi}{4}$
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Answer

$\text{LHS}=\sqrt{2+\sqrt{2+2\cos4\text{x}}}$ $=\sqrt{2+\sqrt{2(1+\cos4\text{x})}}$ $=\sqrt{2+\sqrt{2.2\cos^22\text{x}}}$ $=\sqrt{2+2\cos2\text{x}}$ $=\sqrt{2(1+\cos2\text{x})}$ $=\sqrt{2.2\cos ^2\text{x}}$ $=2\cos\text{x}=\text{RHS}$

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