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If alpha,beta,gamma are acute angle such...

If `alpha,beta,gamma` are acute angle such that `cos alpha = tan beta,cos beta = tan gamma and cos gamma = tan alpha,` then

Answer

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Knowledge Check

  • If alpha,beta and gamma are acute angled such that sin alpha = sqrt3/2 cos beta = sqrt3/2and tan gamma = 1 , then what is alpha+ beta + gamma equal to ?

    A
    `105^@`
    B
    `120^@`
    C
    `135^@`
    D
    `150^@`

  • If alpha,beta, gamma are any three angles , then cos alpha + cos beta - cos gamma - cos (alpha+beta+gamma)=

    A
    `4 cos ( alpha+beta)/(2) cos (beta+gamma)/(2) cos (gamma+alpha)/(2)`
    B
    `4 cos (alpha +beta)/(2) sin (beta+gamma)/(2) sin (gamma + alpha)/(2)`
    C
    `4 cos (alpha+beta)/(2) sin (beta- gamma)/(2) sin ( gamma-alpha)/(2)`
    D
    `4 sin (alpha + beta)/(2) cos (gamma + alpha)/(2)`

  • 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)`

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    If alpha, beta, gamma are acute angles and cos theta = sin beta//sin alpha, cos phi = sin gamma//sin alpha and cos(theta-phi)=sin beta sin gamma then the value of of tan^(2)alpha - tan^(2)beta- tan^(2)gamma is equal to

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