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CBSE Class 12-science Answered

  differentiate tan-1 (x/(1-x2)1/2) wrt cos-1 (2x2 – 1) explain in great detail
Asked by haroonrashidgkp | 13 Aug, 2018, 08:46: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight u equals tan to the power of negative 1 end exponent open parentheses fraction numerator straight x over denominator square root of 1 minus straight x squared end root end fraction close parentheses straight x equals sinθ rightwards double arrow straight theta equals sin to the power of negative 1 end exponent straight x straight u equals tan to the power of negative 1 end exponent open parentheses fraction numerator sinθ over denominator square root of 1 minus sin squared straight theta end root end fraction close parentheses straight u equals tan to the power of negative 1 end exponent open parentheses sinθ over cosθ close parentheses straight u equals tan to the power of negative 1 end exponent open parentheses tan straight theta close parentheses straight u equals straight theta straight u equals sin to the power of negative 1 end exponent straight x du over dx equals fraction numerator 1 over denominator square root of 1 minus straight x squared end root end fraction.......... left parenthesis straight i right parenthesis straight v equals cos to the power of negative 1 end exponent open parentheses 2 straight x squared minus 1 close parentheses straight x equals cosθ rightwards double arrow straight theta equals cos to the power of negative 1 end exponent straight x straight v equals cos to the power of negative 1 end exponent open parentheses 2 cos squared straight theta minus 1 close parentheses straight v equals cos to the power of negative 1 end exponent open parentheses cos 2 straight theta close parentheses straight v equals 2 straight theta straight v equals 2 cos to the power of negative 1 end exponent straight x dv over dx equals fraction numerator negative 2 over denominator square root of 1 minus straight x squared end root end fraction.......... left parenthesis ii right parenthesis du over dv equals fraction numerator fraction numerator 1 over denominator square root of 1 minus straight x squared end root end fraction over denominator fraction numerator negative 2 over denominator square root of 1 minus straight x squared end root end fraction end fraction du over dv equals fraction numerator negative 1 over denominator 2 end fraction end style
Answered by Sneha shidid | 14 Aug, 2018, 05:07: PM

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