IIT JEE 2008 P1 Q2

2 Answers

cos(cot^-1x)=x/√x²+1

sin(cot^-1x)=1/√x²+1

after putting the values we get

x√1+x²

as 0<x<1 cot^{-1}x=cos^{-1}\frac{x}{\sqrt{1+x^{2}}}=sin^{-1}\frac{1}{\sqrt{1+x^{2}}}
hecne the given expression reduces to
x\sqrt{1+x^{2}}

hecne option c

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