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

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

(1+cosalphacosbeta)^2-(cosalpha+cosbeta)^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 cosalpha+cosbeta=0=sinalpha+sinbeta , then cos2alpha+cos2beta=?

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

Show that: sin^2 alpha + sin^2 beta + 2sinalpha sinbeta cos(alpha+beta)=sin^2 (alpha+beta)

If cos alpha+cos beta=0=sin alpha+sinbeta, then cos2alpha+cos 2beta=

|{:(1,cos alpha, cos beta),(cos alpha, 1,cosgamma),(cosbeta,cosgamma,1):}|=|{:(0,cosalpha,cosbeta),(cosalpha,0,cosbeta),(cosbeta,cosgamma,0):}| if cos^(2)alpha+cos^(2)beta+cos^(2)gamma=