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cot^(-1)9+cosec^(-1)(sqrt(41))/(4)=...

`cot^(-1)9+cosec^(-1)(sqrt(41))/(4)=`

A

`pi/6`

B

`pi/4`

C

`pi/3`

D

`(3pi)/4`

Text Solution

Verified by Experts

The correct Answer is:
B
`"cosec"^(-1)x=cot^(-1)sqrt(x^(2)-1) rArr "cosec"^(-1)sqrt(41)/4=cot^(-1)sqrt(41/16-1)=cot^(-1)5/4`
`therefore cot^(-1)9+cot^(-1)5/4=tan^(-1)1/9+tan^(-1)4/5=tan^(-1)(1/9+4/5)/(1-1/9 xx 4/5) = tan^(-1)1=pi/4`.
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