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The value of lim(|x| rarr oo) cos (tan^(...

The value of `lim_(|x| rarr oo) 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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