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