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Trigonometric Ratios Of Compounds — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Ratios Of Compounds1 Mark
Question
Prove that: $\sqrt{\frac{1-\cos2\text{x}}{1+\cos2\text{x}}}=\tan\text{x}$
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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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