`|(cosalphacosbeta,cosalpha sinbeta , - sin alpha),(-sin beta,cosbeta,0),(sinalphacosbeta,sinalpha sinbeta,cosalpha)|`

Evaluate |{:(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta,cosbeta,0),(sinalphacosbeta,sinalphasinbeta,cosalpha):}|

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

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

Evaluate |[cosalpha cosbeta,cosalpha sinbeta,-sinalpha],[-sinbeta,cosbeta,0],[sinalpha cosbeta,sinalpha sinbeta,cosalpha]|

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

Evaluate |[cosalphacosbeta,cosalphasinbeta,-sinalpha],[-sinbeta,cosbeta,0],[sinalphcosbeta,sinalphasinbeta,cosalpha]|

(cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2 =

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

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