I f space u equals space sin open parentheses m cos to the power of minus 1 end exponent x close parentheses space a n d space v equals space cos open parentheses m sin to the power of minus 1 end exponent x close parentheses space p r o v e space t h a t space fraction numerator d u over denominator d v end fraction space equals square root of fraction numerator 1 minus space u squared over denominator 1 space minus space v squared end fraction end root

Asked by inderjeet.saluja | 23rd Aug, 2014, 10:29: PM

Expert Answer:

fraction numerator d u over denominator d x end fraction equals minus fraction numerator cos left parenthesis m space cos to the power of minus 1 end exponent x right parenthesis over denominator square root of 1 minus x squared end root end fraction........ left parenthesis i right parenthesis fraction numerator d v over denominator d x end fraction equals minus fraction numerator sin left parenthesis m sin to the power of minus 1 end exponent x right parenthesis over denominator square root of 1 minus x squared end root end fraction.......... left parenthesis i i right parenthesis left parenthesis i right parenthesis divided by left parenthesis i i right parenthesis comma fraction numerator d u over denominator d v end fraction equals fraction numerator cos left parenthesis m cos to the power of minus 1 end exponent x right parenthesis over denominator sin left parenthesis m sin to the power of minus 1 end exponent x right parenthesis end fraction rightwards double arrow fraction numerator d u over denominator d v end fraction equals fraction numerator square root of 1 minus sin squared left parenthesis m cos to the power of minus 1 end exponent x right parenthesis end root over denominator square root of 1 minus cos squared left parenthesis m sin to the power of minus 1 end exponent x right parenthesis end root end fraction rightwards double arrow fraction numerator d u over denominator d v end fraction equals fraction numerator square root of 1 minus u squared end root over denominator square root of 1 minus v squared end root end fraction rightwards double arrow fraction numerator d u over denominator d v end fraction equals square root of fraction numerator 1 minus u squared over denominator 1 minus v squared end fraction end root H e n c e space P r o v e d

Answered by Prasenjit Paul | 25th Aug, 2014, 10:31: AM

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