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Write the simplest form of tan^(-1) [( 3...

Write the simplest form of `tan^(-1) [( 3 cos x - 4 sin x )/( 4 cos x + 3 sin x) ]`, if `(3)/(4) tan x gt -1`

Text Solution

Verified by Experts

The correct Answer is:
`tan^(-1) (3//4) - x`
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Knowledge Check

  • If y = tan^(-1) ((a cos x - b sin x)/(b cos x + a sin x)) , then dy/dx =

    A
    2
    B
    (-1)
    C
    a/b
    D
    b/a

  • If f(x) = tan^(-1) ((4cosx - 3 sin x)/(3 cos x + 4 sin x)) then f^(')(x) =

    A
    1
    B
    (-1)
    C
    (1/2)
    D
    0

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

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

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