Evaluate `Delta=|{:(0,sinalpha,-cosalpha),(-sinalpha,0, sin beta),(cosalpha,-sinbeta,0):}|`

Evaluate: =|[0,sinalpha,-cosalpha],[-sinalpha,0,sinbeta],[cosalpha,-sinbeta,0]|

Evaluate Delta=|0sinalpha-cosalpha-sinalpha0sinbetacosalpha-sinbeta0|

Show without expanding at any stage that: [0,sinalpha-cosalpha],[-sinalpha,0,sinbeta],[cosalphas-sinbeta,0]|=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

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

Without expanding evaluate the determinant |[sinalpha,cosalpha,sin(alpha+delta)],[sinbeta,cosbeta,sin(beta+delta)],[singamma,cosgamma,sin(gamma+delta)]|

Without expanding evaluate the determinant |[sinalpha,cosalpha,sin(alpha+delta)],[sinbeta,cosbeta,sin(beta+delta)],[singamma,cosgamma,sin(gamma+delta)]|

Evaluate |{:(cos alpha cos beta,,cos alphasinbeta,,-sinalpha),(-sinbeta,,cos beta,,0),(sinalpha cos beta,,sinalphasinbeta,,cos alpha):}|

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

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