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Some Applications Of Trigonometry

Question
CBSEENMA10007735
Wired Faculty App

Prove the following identities where the angles involved are acute angles for which the expressions are defined.
fraction numerator cosA over denominator 1 plus sinA end fraction plus fraction numerator 1 plus sinA over denominator cosA end fraction equals space 2 space secA.

Solution

L.H.S. = fraction numerator cosA over denominator 1 plus sinA end fraction plus fraction numerator 1 plus sinA over denominator cosA end fraction
equals space fraction numerator cos squared straight A plus left parenthesis 1 plus sinA right parenthesis squared over denominator left parenthesis 1 plus sinA right parenthesis space cos space straight A end fraction equals space fraction numerator cos squared straight A plus 1 plus sin squared straight A plus 2 space sinA over denominator left parenthesis 1 plus sinA right parenthesis space cosA end fraction equals space fraction numerator left parenthesis cos squared straight A plus sin squared straight A right parenthesis space plus space 2 space sinA space plus space 1 over denominator left parenthesis 1 plus sinA right parenthesis space cosA end fraction equals space fraction numerator 1 plus 2 space sinA space plus space 1 over denominator left parenthesis 1 plus sinA right parenthesis space cosA end fraction space equals space fraction numerator 2 plus 2 space sinA over denominator left parenthesis 1 plus sinA right parenthesis space cosA end fraction equals space fraction numerator 2 space left parenthesis 1 plus sin space straight A right parenthesis over denominator left parenthesis 1 plus sin space straight A right parenthesis space cos space straight A end fraction equals 2 over cosA equals space 2 space sec space straight A space equals space straight R. straight H. straight S. Hence comma space straight L. straight H. straight S. space equals space straight R. straight H. straight S.

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