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If cos^(-1)((1-x^(2))/(1+x^(2)))+sin^(-1...

If `cos^(-1)((1-x^(2))/(1+x^(2)))+sin^(-1)((2x)/(1+x^(2)))=p` for all `x in[-1,0]`, then p is equal to

A

`(-pi)/(2)`

B

0

C

`(pi)/(2)`

D

`(2pi)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
For `x in [-1,0],cos^(-1)((1-x^(2))/(1+x^(2)))=-2 tan^(-1)x`
and `sin^(-1)((2x)/(1+x^(2)))=2 tan^(-1)x`
`therefore p=0 AA x in [-1,0]`
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