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If y=sec^-1((√x-1)/(x+√x))+sin_1((x+√x)/(√x-1)), - Mathematics and Statistics

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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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Solution

 (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`

Concept: The Concept of Derivative - Derivative of Inverse Function
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