Trig1.14

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Prove that \frac{\tan A}{\sec A-1}+\frac{\tan A}{\sec A+1}=2\csc A\,

LHS=\frac{\tan A(\sec A+1)+\tan A(\sec A-1)}{(\sec A+1)(\sec A-1)}\,

\frac{\tan A \sec A+\tan A+\tan A \sec A-\tan A}{sec^2 A-1}\,

\frac{2\sec A \tan A}{\tan^2 A}\,

\frac{2\sec A}{\tan A}=\frac{2\cos A}{\cos A \sin A}\,

\frac{2}{\sin A}=2\csc A\,=RHS


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