Trig1.8

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Simplify \sqrt{\frac{1+\sin A}{1-\sin A}}=\sec A+\tan A\,

Rationalizing the denominator in LHS,we get

LHS=\sqrt{\frac{(1+\sin A)^2}{(1+\sin A)(1-\sin A)}}=\sqrt{\frac{(1+\sin A)^2}{1-\sin^2 A}}\,

\frac{1+\sin A}{\sqrt{\cos^2 A}}=\frac{1+\sin A}{\cos A}=\frac{1}{\cos A}+\frac{\sin A}{\cos A}=\sec A+\tan A\,=RHS


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