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Question
Prove that: \[\frac{\sin 2x}{1 + \cos 2x} = \tan x\]
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Solution
\[LHS = \frac{\sin2x}{1 + \cos2x}\]
\[ = \frac{2\sin x \times \cos x}{1 + 2 \cos^2 x - 1} \] `[∵ sin 2 x = 2 sin x xx cos x and cos 2x = 2 cos ^2 x -1]`
`= (2 sin x xx cos x) /( 2 cos x xx cos x )`
` = (sin x) / (cos x) `
` = tan x = RHS`
\[\text{ Hence proved } .\]
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