Trigonometry - Proving and Simplifying Trigonometric Identities

Trigonometry - Proving and Simplifying Trigonometric Identities

Prove the identity \(\frac{2 + 2 \sin x - \cos^2 x}{\sin x} = \operatorname{cosec}\ x + 2 + \sin x\).

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Answer:\(\frac{2+2\sin x-\cos^2x}{\sin x}=\operatorname{cosec}x+2+\sin x\), for \(\sin x\ne0\).

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