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cot^(-1)(-1/2)+cot^(-1)(-1/3) is equal t...

`cot^(-1)(-1/2)+cot^(-1)(-1/3)` is equal to

A

`(3pi)/4`

B

`(5pi)/4`

C

`(pi)/4`

D

`(-3pi)/4`

Text Solution

Verified by Experts

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