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Show that: tan^(-1)[ (sqrt(1+cosx)+sqrt(...

Show that: `tan^(-1)[ (sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))] =(pi)/(4)+(x)/(2), x in [0, pi]`

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Knowledge Check

  • Simplest form of tan^(-1)((sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))), pi lt x lt (3pi)/2 is :

    A
    `pi/4 - x/2`
    B
    `(3pi)/2-x/2`
    C
    `-x/2`
    D
    `pi-x/2`

  • intcot^(-1)sqrt((1+cosx)/(1-cosx))dx=

    A
    `(x^(2))/(4)+c`
    B
    `(x^(2))/(2)+c`
    C
    `(x)/(4)+c`
    D
    `(x)/(2)+c`

  • int(sqrt(1+cosx))/(1-cosx)dx=

    A
    `-sqrt2 cosec((x)/(2))+c`
    B
    `sqrt2 cos ((x)/(2))+c`
    C
    `-sqrt2 sec((x)/(2))+c`
    D
    `log[cos((x)/(2))]+c`

    • Similar Questions

    Explore conceptually related problems

    If x in (pi, 2pi) , prove that ((sqrt(1+cosx))+(sqrt(1-cos x)))/((sqrt(1+cos x)) -sqrt(1-cos x)) = cot(pi/4 +x/2)

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

    Prove that tan^(-1)(sqrt((1-cosx)/(1+cosx))=x/2, x lt pi .

    int_(0)^(pi//2)(sqrt(sinx))/((sqrt(sinx)+sqrt(cosx)))dx=(pi)/(4)

    If (sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))=cot(a+x/2) and x in (pi,2pi) then 'a' is equal to :

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