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Evaluate |(cosalphacosbeta,cosalphasinbe...

Evaluate `|(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta,cosbeta,0),(sinalphacosbeta,sinalphasinbeta,cosalpha)|`

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To evaluate the determinant \[ D = \begin{vmatrix} \cos \alpha \cos \beta & \cos \alpha \sin \beta & -\sin \alpha \\ -\sin \beta & \cos \beta & 0 \\ \sin \alpha \cos \beta & \sin \alpha \sin \beta & \cos \alpha \end{vmatrix} ...
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Explore conceptually related problems

Ecaluate [{:(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta,cosbeta,0),(sinalphacosbeta,sinalphasinbeta,cosalpha):}]

Prove that |[cos alpha cos beta, cos alpha sin beta , sin alpha],[-sinbeta,cosbeta,0],[sinalpha cosbeta, sinalpha sinbeta, cos alpha]|=cos2alpha

Knowledge Check

  • |(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta,cosbeta,0),(sinalphacosbeta,sinalphasinbeta,cosalpha)| is equal to

    A
    `sin(alpha+beta)`
    B
    `cos(alpha+beta)`
    C
    0
    D
    1

  • If cosalpha+cosbeta=0=sinalpha+sinbeta , then cos2alpha+cos2beta=?

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

  • The determinant D=|{:(cos(alpha+beta),-sin(alpha+beta),cos2beta),(sinalpha,cosalpha,sinbeta),(-cosalpha,sinalpha,cosbeta):}| is independent of :-

    A
    `alpha`
    B
    `beta`
    C
    `alpha" and "beta`
    D
    Neihter `alpha"nor"beta`

    • Similar Questions

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    (1+cosalphacosbeta)^2-(cosalpha+cosbeta)^2=

    Evaluate : Delta=|{:(0,sinalpha,-cosalpha),(-sinalpha,0,sinbeta),(cosalpha,-sinbeta,0):}| .

    If A=[(0,sin alpha, sinalpha sinbeta),(-sinalpha, 0, cosalpha cosbeta),(-sinalpha sinbeta, -cosalphacosbeta, 0)] then (A) |A| is independent of alpha and beta (B) A^-1 depends only on beta (C) A^-1 does not exist (D) none of these

    Show by vector method that sin(alpha-beta)=sinalphacosbeta-cosalpha sinbeta.

    Show without expanding at any stage that: | (1,cosalpha-sinalpha, cosalpha+sinalpha),(1,cosbeta-sinbeta,cosbeta+sinbeta),(1, cosgamma-singamma,cosgamma+singamma)| =2 |(1,cosalpha, sinalpha),(1,cosbeta, sinbeta),(1,cosgamma,singamma)|

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