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tan^(-1)((cosx+sinx)/(cos x-sinx))...

`tan^(-1)((cosx+sinx)/(cos x-sinx))`

Text Solution

Verified by Experts

The correct Answer is:
`(pi)/(4)-x`
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If y="tan"^(-1)((cosx-sinx)/(cosx+sinx)) , then (dy)/(dx)=

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Knowledge Check

  • If y=tan^(-1)(( sin x + cosx)/(cosx-sinx)) then (dy)/(dx) is equal to

    A
    0
    B
    `(1)/(2)`
    C
    `(pi)/(4)`
    D
    1

  • int dx/(1-cosx -sinx) =

    A
    `log (1+cot (x/2)+c`
    B
    `log (1-tan (x/2)+c`
    C
    `log (1-cot (x/2)+c`
    D
    `log (1+tan (x/2)+c`

  • d/dx {(cosx + sinx)/(cos x - sin x)} =

    A
    1/(cosx-sinx)
    B
    2/(cosx-sinx)
    C
    2/(1-sin2x)
    D
    2/(1-cos2x)

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