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

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Ratios Of Compound Angles1 Mark
Question
Prove that:
$\sqrt{\frac{1-\cos2\text{x}}{1+\cos2\text{x}}}=\tan\text{x}$
✓

Answer

We have,
$\text{LHS}=\sqrt{\frac{1-\cos2\text{x}}{1+\cos2\text{x}}}$
$\sqrt{\frac{1-\cos2\text{x}}{1+\cos2\text{x}}}=\sqrt{\frac{2\sin^2\text{x}}{2\cos^2\text{x}}}$
$=\frac{\sin\text{x}}{\cos\text{x}}$
$\tan\text{x}=\text{RHS.}$

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