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The value of sin^(-1) {( sin. pi/3) x/sq...

The value of `sin^(-1) {( sin. pi/3) x/sqrt((x^(2) + k^(2) - kx))} - cos^(_1) {( cos. pi/6) x/sqrt((x^(2) + k^(2) - kx))}" , where" (k/2 lt x lt 2k, k gt 0)` is

A

`tan^(-1) ((2x^(2) + sk - k^(2))/(x^(2) - 2xk + k^(2)))`

B

`tan^(-1) ((x^(2) + 2xk - 2k^(2))/(x^(2) -2xk - k^(2)))`

C

` tan^(-1) ((x^(2)+2xk - 2k^(2))/( 2x^(2) - 2xk+ 2k^(2)))`

D

None of the above

Text Solution

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The correct Answer is:
D
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