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Given that , tan^(-1) ((2x)/(1-x^(2)))...

Given that ,
`tan^(-1) ((2x)/(1-x^(2))) = {{:(2 tan^(-1) x"," |x| le 1),(-pi +2 tan^(-1)x","x gt 1),(pi+2 tan^(-1)x"," x lt -1):}`
`sin^(-1)((2x)/(1+x^(2))) ={{:(2 tan^(-1)x","|x|le1),(pi -2 tan^(-1)x","x gt 1 and ),(-(pi+2tan^(-1))","x lt -1):}`
`sin^(-1) x + cos^(-1) x = pi//2 " for " - 1 le x le 1`
If `(x -1)(x^(2) +1) gt 0", then " sin(1/2 tan^(-1) .(2x)/(1-x^(2)) tan^(-1) x)` is equal to

A

1

B

`1/sqrt2`

C

`-1`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
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