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Question
Prove the following identities
Solution
\[\text{ LHS }= \frac{2\sin x \cos x - \cos x}{1 - \sin x + \sin^2 x - \cos^2 x}\]
\[ = \frac{\cos x(2\sin x - 1)}{2 \sin^2 x - \sin x} \left( \because 1 - \cos^2 x = \sin^2 x \right)\]
\[ = \frac{\cos x(2\sin x - 1)}{\sin x\left( 2\sin x - 1 \right)}\]
\[ = \cot x \]
= RHS
Hence proved.
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