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Home / Doubts and Solutions/JEE/Mathematics

Prove the following identity.

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Asked by Anish 16th June 2018, 4:42 PM
Answered by Expert
Answer:
begin mathsize 16px style LHS space equals space fraction numerator 1 plus cosx plus sinx over denominator 1 plus cosx minus sinx end fraction equals fraction numerator 1 plus cosx plus sinx over denominator 1 plus cosx minus sinx end fraction cross times fraction numerator 1 minus cosx minus sinx over denominator 1 minus cosx minus sinx end fraction equals fraction numerator 1 minus open parentheses sinx plus cosx close parentheses squared over denominator 1 minus cosx minus sinx plus cosx minus cos squared straight x minus cosxsinx minus sinx plus sinxcosx plus sin squared straight x end fraction equals fraction numerator 1 minus open parentheses sin squared straight x plus cos squared straight x plus 2 sinxcosx close parentheses over denominator 1 minus cosx minus sinx plus cosx minus cos squared straight x minus cosxsinx minus sinx plus sinxcosx plus sin squared straight x end fraction equals fraction numerator 1 minus open parentheses 1 plus 2 sinxcosx close parentheses over denominator 1 minus sinx minus cos squared straight x minus sinx plus sin squared straight x end fraction equals fraction numerator negative 2 sinxcosx over denominator 1 plus sin squared straight x minus 2 sinx minus open parentheses 1 minus sin squared straight x close parentheses end fraction equals fraction numerator negative 2 sinxcosx over denominator 2 sin squared straight x minus 2 sinx end fraction equals fraction numerator negative 2 sinxcosx over denominator 2 sinx left parenthesis sinx minus 1 right parenthesis end fraction equals fraction numerator cosx over denominator 1 minus sinx end fraction equals RHS end style
Answered by Expert 18th June 2018, 10:16 AM
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