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The solution of the equation cos ^(2) x ...

The solution of the equation `cos ^(2) x - 2 cos x = 4 sin x ` is `+4 sin ^(2) x (0 le x le pi)`

A

`pi + tan ^(-1) ((-1)/(2))`

B

`pi - cot^(-1) ((1)/(2))`

C

`pi - tan ^(-1) 2`

D

none of these

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The correct Answer is:
A
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Knowledge Check

  • The solution of the equation "cos"^(2) x-2 "cos" x = 4 "sin" x - "sin" 2x (0 le x le pi) , is

    A
    `pi-"cot"^(-1)(1)/(2)`
    B
    `pi - "tan"^(-1) 2`
    C
    `pi + "tan"^(-1) (-(1)/(2))`
    D
    none of these

  • The number of real solution of the equation sqrt(1 + cos 2x) = sqrt2 sin^(-1) (sin x), -pi le x le pi , is

    A
    0
    B
    1
    C
    2
    D
    infinite

  • The solutions of the equation 1+(sin x - cos x)"sin" pi/4=2 "cos"^(2) (5 x)/2 is/are

    A
    `x=(n pi)/3+pi/8, n in Z`
    B
    `x=(npi)/2+(5pi)/16, n in Z`
    C
    `x=(npi)/3+pi/4, n in Z`
    D
    `x=(npi)/2+(7pi)/8, n in Z`

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