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)`

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

1.	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)`
Answer» Correct Answer - 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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