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Let f(x) = {(sin (tan^(-1) x) + sin (cot...

Let `f(x) = {(sin (tan^(-1) x) + sin (cot^(-1) x)}^2 - 1`, where `|x| gt 1` and `dy/dx = 1/2 d/dx (sin^(-1) f(x))`. If `y(sqrt3) = pi/6` then `y( -sqrt3)`

A

`-(pi)/(6)`

B

`(2pi)/(3)`

C

`(pi)/(3)`

D

`(5pi)/(6)`

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The correct Answer is:
A
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