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{SinA/1+cosA +1+CosA/sinA} {cosA/1+sinA + 1+sinA/cosA}=4 secA.cosecA

Asked by Sharan9958 | 26 Feb, 2019, 07:41: AM

Expert Answer

begin mathsize 12px style open square brackets fraction numerator begin display style sin A end style over denominator begin display style 1 plus cos A end style end fraction plus fraction numerator begin display style 1 plus cos A end style over denominator begin display style sin A end style end fraction close square brackets open square brackets fraction numerator cos A over denominator 1 plus sin A end fraction plus fraction numerator 1 plus sin A over denominator cos begin display style A end style end fraction close square brackets equals space open square brackets fraction numerator begin display style sin squared A plus open parentheses 1 plus cos A close parentheses squared end style over denominator open parentheses 1 plus cos A close parentheses begin display style open parentheses sin A close parentheses end style end fraction close square brackets open square brackets fraction numerator begin display style cos squared A plus open parentheses 1 plus sin A close parentheses squared end style over denominator open parentheses 1 plus sin A close parentheses begin display style cos end style begin display style A end style end fraction close square brackets equals open square brackets fraction numerator 2 plus 2 cos A over denominator open parentheses 1 plus cos A close parentheses open parentheses sin A close parentheses end fraction close square brackets open square brackets fraction numerator 2 plus 2 sin A over denominator open parentheses 1 plus sin A close parentheses cos A end fraction close square brackets space equals space fraction numerator 2 over denominator sin begin display style A end style end fraction cross times fraction numerator 2 over denominator cos begin display style A end style end fraction space equals space 4 space s e c A space cos e c A end style

Answered by Thiyagarajan K | 26 Feb, 2019, 09:49: AM

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