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If Sin^(-1)x + Sin^(-1)y + Sin^(-1)z = p...

If `Sin^(-1)x + Sin^(-1)y + Sin^(-1)z = pi`, then prove that `x^(4) + y^(4) + z^(4) + 4x^(2)y^(2)z^(2) = 2(x^(2)y^(2)+y^(2)z^(2)+z^(2)x^(2))`.

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Knowledge Check

  • If sin^(-1)x +sin^(-1)y+sin^(-1)z=pi then x^(4)+y^(4)+z^(4)+4x^(2)y^(2)z^(2)=

    A
    `x^(2)y^(2)+y^(2)z^(2)+z^(2)x^(2)`
    B
    `2x^(2)y^(2)z^(2)`
    C
    `2xyz`
    D
    `2(x^(2)y^(2)+y^(2)z^(2)+z^(2)x^(2))`

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

    A
    0
    B
    1
    C
    xyz
    D
    2xyz

  • If Sin^(-1)x+Sin^(-1)y+Sin^(-1)z=(3pi)/2 , then the value of x^(100)+y^(100)+z^(100)-9/(x^(101)+y^(101)+z^(101))

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    B
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    C
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    D
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