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Prove that: tan^(-1){(sqrt(1+cosx)+sqrt(...

Prove that: `tan^(-1){(sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))}=pi/4-x/2,\ if\ pi < x <\3pi/2`

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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`

  • 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`

  • 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`

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