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  • Prove the following identities, where the angles involved are acute angles for which the expressions are defined. sqrt frac1+sin A /1-sin A= secA+tan A

5. Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

   (vi)\sqrt{\frac{1+\sin A}{1-\sin A}}= \sec A+\tan A

Answers (1)

best_answer

We need to prove -
\sqrt{\frac{1+\sin A}{1-\sin A}}= \sec A+\tan A
Taking LHS;
By rationalising the denominator, we get;

\\= \sqrt{\frac{1+\sin A}{1-\sin A}\times \frac{1+\sin A}{1+\sin A}}\\\\ = \sqrt{\frac{(1+\sin A)^2}{1-\sin^2A}}\\\\ =\frac{1+\sin A}{\cos A}\\\\ = \sec A + \tan A\\\\ = RHS

Hence proved.

 

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manish

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