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Find the number of ordered pairs (x,y) s...

Find the number of ordered pairs (x,y) satisfying the equations `sin^(-1)x+sin^(-1)y=(2pi)/3` and `cos^(-1)x-cos^(-1)y=-(pi)/3`

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If sin^(-1)x+sin^(-1)y=(pi)/2 and sin2x=cos3y , then

Knowledge Check

  • If Sin^(-1)x+Sin^(-1)y=2pi//3,"then "Cos^(-1)x+Cos^(-1)y=

    A
    `2pi//3`
    B
    `pi//3`
    C
    `pi//6`
    D
    `pi`

  • The number of solution of (x,y) so that sin^(-1)x+sin^(-1)y=(2pi)/3,cos^(-1)x-cos^(-1)y=-(pi)/3 is

    A
    1
    B
    2
    C
    3
    D
    0

  • Point P(x,y) satisfying the equation sin^(-1)x+cos^(-1)y+cos^(-1)(2xy)=(pi)/2 lies on

    A
    the bisector of the first and third quadrant
    B
    bisector of the second and fourth quadrant.
    C
    the rectangle formed by the lines `x=+-1` and `y=+-1`
    D
    a unit circle with centre at the origin.

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