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The value of cos [tan^-1 {sin (cot^-1 x)...

The value of `cos [tan^-1 {sin (cot^-1 x)}]` is

A

`sqrt((x^(2)+1)/(x^(2)-1))`

B

`sqrt((1-x^(2))/(x^(2)+2))`

C

`sqrt((1-x^(2))/(1+x^(2)))`

D

`sqrt((x^(2)+1)/(x^(2)+2))`

Text Solution

Verified by Experts

The correct Answer is:
D
`cos[tan^(-1){sin(cot^(-1)x)}]`
`=cos[tan^(-1){sin("sin"^(-1)(1)/(sqrt(1+x^(2))))}]`
`=cos[tan^(-1)((1)/(sqrt(1+x^(2))))]`
`=cos[cos^(-1)sqrt((1+x^(2))/(2+x^(2)))]`
`=sqrt((1+x^(2))/(2+x^(2)))`
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