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The value of underset( |x| -> infty) lim...

The value of `underset( |x| -> infty) lim cos( tan^(-1)(sin(tan^(-1)x)))`is equal to

A

`-1`

B

`sqrt2`

C

`-(1)/(sqrt2)`

D

`(1)/(sqrt2)`

Text Solution

Verified by Experts

The correct Answer is:
D
underset(|x| rarr oo)("lim") cos (tan^(-1) (sin (tan^(-1) x)))`
`= cos (tan^(-1) (sin (tan^(-1) oo)))`
`= cos (tan^(-1) (sin ((pi)/(2))))`
`= cos (tan^(-1) (1)) = cos ((pi)/(4))`
`= (1)/(sqrt2)`
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