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ICSE Class 10 Answered

sin a/cot a + cosec a =2+sin a/cot a-cosec a. prove.(please give me ans. as fast as possible.)
 
Asked by muskangupta6162 | 14 Apr, 2016, 09:02: PM
answered-by-expert Expert Answer
LHS equals fraction numerator sina over denominator cota plus coseca end fraction space space space space space space space equals fraction numerator sina over denominator begin display style cosa over sina end style plus begin display style 1 over sina end style end fraction space space space space space space space equals fraction numerator sin squared straight a over denominator begin display style cosa plus 1 end style end fraction space space space space space space space equals fraction numerator sin squared straight a left parenthesis 1 minus cosa right parenthesis over denominator begin display style left parenthesis 1 plus cosa right parenthesis left parenthesis 1 minus cosa right parenthesis end style end fraction space space space space space space space equals fraction numerator sin squared straight a left parenthesis 1 minus cosa right parenthesis over denominator begin display style 1 minus cos squared straight a end style end fraction space space space space space space space equals fraction numerator sin squared straight a left parenthesis 1 minus cosa right parenthesis over denominator begin display style sin squared straight a end style end fraction.... left parenthesis Since space sin squared straight a plus cos squared straight a equals 1 right parenthesis space space space space space space space equals 1 minus cosa RHS equals 2 plus fraction numerator sina over denominator cota minus coseca end fraction space space space space space space space equals 2 plus fraction numerator sina over denominator begin display style cosa over sina minus 1 over sina end style end fraction space space space space space space space equals 2 plus fraction numerator sin squared straight a over denominator begin display style cosa minus 1 end style end fraction space space space space space space space equals 2 minus fraction numerator sin squared straight a over denominator begin display style 1 minus cosa end style end fraction space space space space space space space equals 2 minus fraction numerator sin squared straight a left parenthesis 1 plus cosa right parenthesis over denominator begin display style left parenthesis 1 minus cosa right parenthesis left parenthesis 1 plus cosa right parenthesis end style end fraction space space space space space space space equals 2 minus fraction numerator sin squared straight a left parenthesis 1 plus cosa right parenthesis over denominator begin display style 1 minus cos squared straight a end style end fraction space space space space space space space equals 2 minus fraction numerator sin squared straight a left parenthesis 1 plus cosa right parenthesis over denominator begin display style sin squared straight a end style end fraction.... left parenthesis Since space sin squared straight a plus cos squared straight a equals 1 right parenthesis space space space space space space space equals 2 minus left parenthesis 1 plus cosa right parenthesis space space space space space space space equals 1 minus cosa equals LHS Hence space proved.
Answered by Rebecca Fernandes | 15 Apr, 2016, 09:09: AM
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