Exam-Style Problem
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Problem 11
11
☆
Prove the identity
\(\sin x+\cos x\cot x \equiv \csc x\).
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Solution
\[ \sin x+\cos x\cot x=\sin x+\cos x\cdot\frac{\cos x}{\sin x} =\frac{\sin^2x+\cos^2x}{\sin x} =\frac{1}{\sin x}=\csc x. \]
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