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tan^(-1)sqrt(x) is equal to...

`tan^(-1)sqrt(x)` is equal to

A

`(1)/(2)"cos"^(-1)(1-x)/(1+x)`

B

`(1)/(2)"cos"^(-1)(1+x)/(1-x)`

C

`(1)/(2)"cos"^(-1)(1)/(x)`

D

`(1)/(2)"cos"^(-1)(1)/(x^(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
`tan^(-1)sqrt(x)=(1)/(2)(2tan^(-1)sqrt(x))`
[multiply and divide by2]
`=(1)/(2)"cos"^(-1){(1-(sqrt(x))^(2))/(1+(sqrt(x))^(2))}`
`[because2tan^(-1)x=cos^(-1)((1-x^(2))/(1+x^(2))),xge0]`
`=(1)/(2)"cos"^(-1)((1-x)/(1+x))`
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