Exam-Style Problem
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Problem 22
22
☆
Prove the identity
\(\displaystyle \frac{1}{1+\cos x}+\frac{1}{1-\cos x}\equiv 2\csc^2x.\)
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Solution
\[ \frac{1}{1+\cos x}+\frac{1}{1-\cos x} =\frac{(1-\cos x)+(1+\cos x)}{1-\cos^2x} =\frac{2}{\sin^2x}=2\csc^2x. \]
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