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प्रश्न
If `y=sec^-1((sqrtx-1)/(x+sqrtx))+sin_1((x+sqrtx)/(sqrtx-1)), `
(A) x
(B) 1/x
(C) 1
(D) 0
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उत्तर
(D)
`Let y=sec^-1((sqrtx-1)/(x+sqrtx))+sin^-1((x+sqrtx)/(sqrtx-1))`
`=cos^-1((x+sqrtx)/(sqrtx-1))+sin^-1((x+sqrtx)/(sqrtx-1)) [because sec^-1(x)=cos^-1(1/x)]`
`therefore y=pi/2`
`dy/dx=d/dx(pi/2)=0`
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