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

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Ratios Of Compound Angles2 Marks
Question
Prove that:
$\sqrt{2+\sqrt{2+2\cos4\text{x}}}=2\cos\text{x},0\cos\text{x},<\text{x}<\frac{\pi}{4}$
✓

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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