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ICSE Class 10 Answered

prove sinA+cosA/(sinA-cosA)   +   sinA-cosA/(sinA+cosA)=1/(sin2A-cos2A)=2/(1-2cos2A)=2sec2A/(tan2A-1)
Asked by Sunita | 05 Apr, 2018, 03:54: PM
answered-by-expert Expert Answer
begin mathsize 16px style fraction numerator sin thin space straight A space plus space cos space straight A over denominator sin thin space straight A space minus space cos space straight A end fraction plus fraction numerator begin display style sin thin space straight A space minus space cos space straight A end style over denominator begin display style sin thin space straight A space plus space cos space straight A end style end fraction
cross space multiply
equals fraction numerator begin display style open parentheses sin thin space straight A space plus space cos space straight A close parentheses squared plus open parentheses sin thin space straight A space minus space cos space straight A close parentheses squared end style over denominator begin display style sin squared thin space straight A space minus space cos squared space straight A end style end fraction
equals fraction numerator 2 over denominator sin squared thin space straight A space minus space cos squared space straight A end fraction
equals fraction numerator begin display style 2 end style over denominator begin display style open parentheses 1 minus cos squared thin space straight A close parentheses space minus space cos squared space straight A end style end fraction

now comma
fraction numerator begin display style 2 end style over denominator begin display style sin squared thin space straight A space minus space cos squared space straight A end style end fraction space divide space by space cos squared straight A
equals fraction numerator begin display style 2 sec squared straight A end style over denominator begin display style tan squared thin space straight A space minus space 1 end style end fraction

end style
Answered by Arun | 05 Apr, 2018, 05:17: PM
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