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If x=r cos alpha cos beta,y=r cos alpha ...

If `x=r cos alpha cos beta,y=r cos alpha sin beta,z=r sin alpha` then `x^(2)+y^(2)+z^(2)`=

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Locus of the point (r sec alpha cos beta,r sec alpha sin beta,r tan alpha) is (a). x^(2)-y^(2)-z^(2)=r^(2) (b). x^(2)-y^(2)+z^(2)=r^(2) (c). x^(2)+y^(2)+z^(2)=r^(2) (d) . x^(2)+y^(2)-z^(2)=r^(2)

If x=r sin alpha cos beta, y= r sin alpha sin beta and z= r cos alpha , prove that x^(2)+y^(2) + z^(2) = r^(2).

Knowledge Check

  • If x= r sin alpha. cos beta, y=r sin alpha. Sin beta and z=r cos alpha , then value of x^(2) + y^(2) is

    A
    `r^(2)`
    B
    `r^(2) + z^(2)`
    C
    `r^(2)-z^(2)`
    D
    `-z^(2)`

  • If x = cos alpha + cos beta - cos(alpha +beta) and y = 4 sin '(alpha)/(2) sin'(beta)/(2) cos((alpha+ beta)/(2)) , then (x-y) equals

    A
    0
    B
    1
    C
    -1
    D
    -2

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    If cos alpha+cos beta=0=sin alpha+sin beta then cos2 alpha+cos2 beta=

    If cos alpha + cos beta =0=sin alpha + sin beta , then cos 2 alpha + cos 2 beta=

    Eliminate alpha , if x = r cos alpha , y = r sin alpha .

    ( cos alpha + cos beta )^(2) + ( sin alpha + sin beta )^(2) =

    ( cos alpha - cos beta )^(2) + ( sin alpha - sin beta )^(2) =

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