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Question
Prove that: \[\sqrt{\frac{1 - \cos 2x}{1 + \cos 2x}} = \tan x\]
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Solution
\[LHS = \sqrt{\frac{1 - \cos 2x}{1 + \cos 2x}}\]
\[ = \sqrt{\frac{2 \sin^2 x}{2 \cos^2 x}} \left[ \because 1 - \cos2x = 2 \sin^2 x \text{ and }1 + \cos2x = 2 \cos^2 x \right]\]
`= (sin x) /(cos x)`
\[ = \tan x = RHS\]
\[\text{ Hence proved } . \]
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