D i f f e r e n t i a t e space sin space open square brackets 2 space tan to the power of minus 1 end exponent space square root of fraction numerator 1 minus x over denominator 1 plus x end fraction end root space close square brackets space space w. r. t. x.

Asked by inderjeet.saluja | 24th Aug, 2014, 05:58: PM

Expert Answer:

y space equals space sin space left square bracket space 2 space tan to the power of space minus 1 end exponent square root of fraction numerator 1 minus x over denominator 1 plus x end fraction end root right square bracket P u t space x equals space cos space theta y space equals space sin space left square bracket space 2 space space tan to the power of space minus 1 end exponent square root of fraction numerator 1 minus cos space theta over denominator 1 plus cos theta end fraction end root right square bracket equals space sin space left square bracket space 2 space space tan to the power of space minus 1 end exponent square root of fraction numerator 2 sin squared begin display style theta over 2 end style over denominator 2 space cos squared begin display style theta over 2 end style end fraction end root right square bracket  equals sin space left square bracket space 2 space space space tan to the power of space minus 1 end exponent square root of tan squared space theta over 2 end root right square bracket equals sin space left square bracket space 2 space space tan to the power of space minus 1 end exponent left parenthesis space tan space theta over 2 right parenthesis right square bracket equals sin space left square bracket 2 theta over 2 right square bracket equals sin space left square bracket space cos space to the power of minus 1 end exponent x right square bracket  fraction numerator d y over denominator d x end fraction equals space cos space left square bracket cos space to the power of minus 1 end exponent x right square bracket space fraction numerator minus 1 over denominator square root of 1 minus x squared end root end fraction

Answered by Sanjana Dhopatkar | 25th Aug, 2014, 09:30: AM

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