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The value of x for which sin(cot^-1(1+x)...

The value of `x` for which `sin(cot^-1(1+x))=cos(tan^-1x)` is

A

`-(1)/(2)`

B

1

C

0

D

`(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`sin["sin"^(-1)(1)/(sqrt((1+x)^(2)+1))]=cos("cos"^(-1)(1)/(sqrt(1+x^(2))))`
`rArr(1)/(sqrt((1+x)^(2)+1)]=(1)/(sqrt(1+x^(2)))`
`rArr(1+x)^(2)+1=1+x^(2)`
`rArr2x+2=0`
`thereforex=-(1)/(2)`
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