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ICSE Class 10 Answered

prove that if secA +tanA =a ,then prove that a^2-1/a^2+1=sinA  
Asked by Gopalsagar6176 | 15 Oct, 2018, 12:49: PM
answered-by-expert Expert Answer
begin mathsize 18px style secA space plus space tan space straight A space equals space straight a
fraction numerator 1 plus space sin space straight A over denominator cos begin display style space end style begin display style straight A end style end fraction equals straight a
fraction numerator straight a squared minus 1 over denominator straight a squared plus 1 end fraction equals fraction numerator begin display style open parentheses fraction numerator 1 plus space sin space straight A over denominator cos begin display style space end style begin display style straight A end style end fraction close parentheses squared minus 1 end style over denominator open parentheses fraction numerator 1 plus space sin space straight A over denominator cos begin display style space end style begin display style straight A end style end fraction close parentheses squared plus 1 end fraction equals fraction numerator 1 plus sin squared straight A plus 2 sin space straight A space minus space cos squared straight A over denominator 1 plus sin squared straight A plus 2 sin space straight A space plus space cos squared straight A end fraction
equals fraction numerator 2 sin squared straight A plus 2 sin space straight A over denominator 2 plus 2 sin space straight A end fraction
equals fraction numerator begin display style sin squared straight A plus sin space straight A end style over denominator begin display style 1 plus sin space straight A end style end fraction
equals sin space straight A end style
Answered by Arun | 16 Oct, 2018, 11:50: AM
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