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Prove that : cot^(-1)((sqrt(1+sinx)+sq...

Prove that :
`cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2,x in(0,pi/4)`

Answer

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If y="tan"^(-1)((sqrt(1+sinx)+sqrt(1-sinx)))/((sqrt(1+sinx)-sqrt(1-sinx)))," find "(dy)/(dx).

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Knowledge Check

  • cot^(-1)((sqrt(1-sinx)+sqrt(1+sinx))/(sqrt(1-sinx)-sqrt(1+sinx)))=...(0ltxltpi/2)

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

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