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If sin^(-1) ((2a)/(1+a^2))+ sin^(-1) ((2...

If `sin^(-1) ((2a)/(1+a^2))+ sin^(-1) ((2b)/(1+b^2)) = 2 tan^(-1)x` then `x=`

A

`(a - b)/(1 + ab)`

B

`(b)/(1 + ab)`

C

`(b)/(1 - ab)`

D

`(a + b)/(1 - ab)`

Text Solution

Verified by Experts

The correct Answer is:
D
Since `sin^(-1) ((2x)/(1 + x^(2))) = 2 tan^(-1) x " for " x in (-1, 1)`
`sin^(-1) ((2a)/(1 + a^(2))) + sin^(-1) ((2b)/(1 + b^(2))) = 2 tan^(-1) x`
`rArr 2 tan^(-1) a + 2 tan^(-1) b = 2 tan^(-1) x`
or `tan^(-1) a + 2 tan^(-1) b = 2 tan^(-1) x`
or `tan^(-1) ((a + b)/(1 -ab)) = tan^(-1) x`
or `x = (a + b)/(1 - ab)`
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