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If 2y=(cot^(-1) ((sqrt3cosx+sinx)/(cosx-...

If `2y=(cot^(-1) ((sqrt3cosx+sinx)/(cosx-sqrt3sinx)))^2, x in (0,pi/2)`

A

`2x-pi/3`

B

`pi/6-x`

C

`x-pi/6`

D

`pi/3-x`

Text Solution

Verified by Experts

The correct Answer is:
C
`2y=(cot^(-1)((cos.((pi)/(6)-x))/(cos.((pi)/(3)+x))))^2`
`2y=(cot^(-1)((cos.((pi)/(6)-x))/(sin.((pi)/(6)-x))))^2`
`2y=(cos^-1(cot(pi/6-x)))^2`
`2y=(pi/6-x)^2," "2y'=-2(pi/6-x)," " y'=x-pi/6`
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