Exam-Style Problem
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Problem 19
19
☆
Prove the identity
\(\displaystyle \frac{1+\tan^2x}{\tan x}\equiv \sec x\,\csc x.\)
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Solution
\[ \frac{1+\tan^2x}{\tan x}=\frac{\sec^2x}{\tan x} =\frac{1/\cos^2x}{\sin x/\cos x} =\frac{1}{\sin x\cos x}=\sec x\,\csc x. \]
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