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Problem 13
13
☆
Prove the identity
\(\csc x-\sin x \equiv \cos x\cot x\).
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Solution
\[ \csc x-\sin x=\frac{1}{\sin x}-\sin x =\frac{1-\sin^2x}{\sin x} =\frac{\cos^2x}{\sin x} =\cos x\cdot\frac{\cos x}{\sin x} =\cos x\,\cot x. \]
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