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If alpha, beta and gamma are angles such...

If `alpha, beta` and `gamma` are angles such that `tanalpha + tanbeta + tangamma= tanalpha tanbeta tangamma` and `x = cosalpha + isinalpha, y = cosbeta+ isinbeta` and `z= cos gamma+ isingamma` then the value of `xyz` is

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Knowledge Check

  • If alpha, beta and gamma are angle such that tan alpha + tan beta+tan gamma= tan alpha tan beta tan gammaand x=cos alpha + I sin alpha, y=cos beta+ I sin beta and z= cos gamma+ I sin gamma, then the value of xyz is -

    A
    1
    B
    `-1`
    C
    0
    D
    `1 or (-1)`

  • IF alpha , beta and gamma are angles such that tan alpha + tan beta + tan gamma = tan alpha tan beta tan gamma and x= cos alpha + i sin alpha , y = cos beta + i sin beta and z= cos gamma + i sin gamma , then xyz =

    A
    1, but not -1
    B
    `-1 ` but not 1
    C
    `+1` or -1
    D
    `0`

  • If tanalpha+tanbeta+tangamma=tanalphatanbetatangamma,then

    A
    `alpha, beta` must be angles of a triangle
    B
    the sum of any two of `alpha, beta,gamma` is equal to the third
    C
    `alpha+beta+gamma` must be an integral multiple of `pi`
    D
    none of these

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    If alpha+beta+gamma=2pi , then show that tan.alpha/2 + tan.beta/2 + tan.gamma/2 = tan.alpha/2 tan.beta/2 tan.gamma/2 .

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    If x=cosalpha+isinalpha,y=cosbeta+isinbeta," then "(x-y)/(x+y)

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