Prove that `(cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2=4cos^2((alpha-beta)/2)dot`

Prove that: (cosalpha-cosbeta)^2+(sinalpha-sinbeta)^2=4sin^2((alpha-beta)/2)^(\ )

Prove that (Cosalpha-Cosbeta)^(2)+(Sinalpha-Sinbeta)^(2)=4Sin^(2)((alpha-beta)/2)

If (cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2=lambdacos^2((alpha-beta)/2), write the value of lambdadot

If cosalpha+cosbeta=0=sinalpha+sinbeta" then "cos2alpha+cos2beta

For all value of alpha,beta,gamma prove that ,cosalpha+cosbeta+cosgamma+cos(alpha+beta+gamma)=4cos(alpha+beta)/2*cos(beta+gamma)/2*cos(gamma+alpha)/2

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

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

(cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2= ............... A) 4 cos ^(2) ((alpha - beta)/(2)) B) 4 sin ^(2) ((alpha - beta)/( 2)) C) 4 cos ^(2) ((alpha + beta)/(2)) D) 4 sin ^(2) ((alpha +beta)/(2))

If cosalpha+cosbeta=1/3 and sinalpha+sinbeta=1/4 prove that cos(alpha-beta)/2=+-5/24

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