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

The value of the determinant Delta = |(cos (alpha + beta),- sin (alpha + beta),cos 2 beta),(sin alpha,cos alpha,sin beta),(- cos alpha,sin alpha,- cos beta)| , is

sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>sin(alpha+beta)

f(alpha,beta) = cos^2(alpha)+ cos^2(alpha+beta)- 2 cosalpha cosbeta cos(alpha+beta) is

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

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

If sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>sin(alpha+beta) =

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

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

If "cot"(alpha+beta)=0, then "sin"(alpha+2beta) can be (a) -sinalpha (b) sinbeta (c) cosalpha (d) cosbeta

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