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Q.

If y=Tan11+x2+1x21+x21x2 for 0<|x|<1 find dydx

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Detailed Solution

Given y=Tan11+x2+1x21+x21x2

put x2=cos2θ

2θ=cos1x2θ=12cos1x2

y=Tan11+cos2θ+1cos2θ1+cos2θ1cos2θ  1+cos2θ=2cos2θ     1cos2θ=2sin2θ    

y=Tan1cosθ+sinθcosθsinθy=Tan11+Tanθ1Tanθ

y=Tan1Tanπ4+θtan1(tanθ)=θ

y=π4+θy=π4+12cos1x2

diff ‘y’ w.r.t. ‘x’ on B.S

dydx=1211x4(2x)=x1x4ddxcos1(x)=11x2

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