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prove that tan^(-1) sqrt x = 1/2 cos^(...

prove that
`tan^(-1) sqrt x = 1/2 cos^(-1)((1-x)/(1+x)), x in [0,1]`

Answer

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Prove the following : tan^(-1)sqrtx=1/2 cos^(-1)((1-x)/(1+x)),x in[0,1]

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Knowledge Check

  • If x in (0,1) then the value of tan^(-1)((1-x^2)/(2x))+cos^(-1)((1-x^2)/(1+x^2)) is equal to a) -pi/2 b)0 c) pi/2 d) pi

    A
    `-pi/2`
    B
    zero
    C
    `pi/2`
    D
    `pi`

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