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

If `sin^(-1)((2a)/(1+a^2))+sin^(-1)((2b)/(1+b^2))=2tan^(-1)x ,` then `x` is equal to `[a , b , in (0,1)]` (a)`(a-b)/(1+a b)` (b) `b/(1+a b)` (c) `b/(1+a b)` (d) `(a+b)/(1-a b)`

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Knowledge Check

  • If sin^(-1)((2a)/(1+a^(2)))+sin^(-1)((2b)/(1+b^(2)))= 2cot^(-1)((1)/(x)) , then x is equal to [AA a, b in (0, 1)]

    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) then x is =2 ta^-1 x, equal to

    A
    `(a-b)/(1+ab)`
    B
    `b/(1+ab)`
    C
    `b/(1-ab)`
    D
    `(a+b)/(1-ab)`

  • If 1/sqrt(2) le x le 1 and sin^(-1)(2xsqrt(1-x^(2))) = A + B sin^(-1)x , then (A,B)=

    A
    `(pi,2)`
    B
    (0,2)
    C
    `(pi,-2)`
    D
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