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The value of cot(cosec^(-1)(5)/(3)+tan^(...

The value of `cot(cosec^(-1)(5)/(3)+tan^(-1)""(2)/(3))` is

A

`(5)/(17) `

B

`(6)/(17)`

C

`(3)/(17)`

D

`(4)/(17)`

Text Solution

Verified by Experts

The correct Answer is:
B
`cot(cosec^(-1)(5)/(3)+tan^(-1)""(2)/(3))`
`=cot(tan^(-1)""(3)/(4)+tan^(-1)""(2)/(3))`
` = cot tan^(-1)[((3)/(4)+(2)/(3))/(1-(1)/(2))]`
` = cot[tan^(-1)((17)/(6))] = (6)/(17)`
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