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  • Prove the following identities, where the angles involved are acute angles for which the expressions are defined. cos A /1+sin A + 1+sin A/cos A = 2 sec A.

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

   (ii) \frac{\cos A}{1+\sin A}+\frac{1+\sin A}{\cos A}= 2\sec A
 

Answers (1)

best_answer

We need to prove-

\frac{\cos A}{1+\sin A}+\frac{1+\sin A}{\cos A}= 2\sec A

taking LHS;
\\=\frac{\cos^2A+1+\sin^2A+2\sin A}{\cos A(1+\sin A)}\\\\ =\frac{2(1+\sin A)}{\cos A(1+\sin A)}\\\\ =2/\cos A = 2\sec A

  = RHS

Hence proved.

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manish

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