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(tan^(-1)(sqrt3)-sec^(-1)(-2))/(cosec^(-...

`(tan^(-1)(sqrt3)-sec^(-1)(-2))/(cosec^(-1)(-sqrt2)+cos^(-1)(-(1)/(2)))` is equal to

A

`(4)/(5)`

B

`-(4)/(5)`

C

`(3)/(5)`

D

0

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Verified by Experts

The correct Answer is:
B
`(tan^(-1)(sqrt3)-(pi-sec^(-1)(2)))/(-cosec^(-1)(sqrt2)+pi-cos^(-1)((1)/(2)))`
`=((pi)/(3)-(pi-(pi)/(3))/(-(pi)/(4)+pi-(pi)/(4))=((2pi)/(3)-x))/(pi-(pi)/(4)-(pi)/(3))`
`=(-(pi)/(3))/((12pi-3pi-4pi)/(12))=(-(pi)/(3))/((5pi)/(12))=-(4)/(5)`
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