Evaluate `|cosalphacosbetacosalphasinbeta-sinalpha-sinbetacosbeta0sinalphacosbetasinalphasinbetacosalpha|`

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

costheta-sintheta=cosalpha-sinalpha

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

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 prove that cos2alpha +cos2beta=-2cos(alpha +beta) .

A square of side ' a ' lies above the x-axis and has one vertex at the origin. The side passing through the origin makes an angle alpha (0ltalphaltpi/ 4) with the positive direction of x-axis. equation its diagonal not passing through origin is: a. y(cosalpha-sinalpha)-x(sinalpha-cosalpha)=a b. y(cosalpha+sinalpha)+x(sinalpha-cosalpha)=a c. y(cosalpha-sinalpha)+x(sinalpha+cosalpha)=a d. y(cosalpha+sinalpha)-x(cosalpha+sinalpha)=a

The expression (sinalpha+sinbeta)/(cosalpha+cosbeta) is equal to

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