Prove that `(cos^2 alpha - cos^2 beta)/(cos^2 alpha*cos^2 beta) = tan^2 beta - tan^2 alpha`

If cos theta=(cos alpha-cos beta)/(1-cos alpha cos beta), prove that tan theta/2=+-tan alpha/2 cot beta/2.

cos 2 alpha =(3 cos 2 beta -1)/( 3-cos 2 beta), then tan alpha=

Prove that : cos^2alpha+cos^2(alpha+beta)-2cosalphacosbetacos(alpha+beta)=sin^2beta

Prove that (sin alpha cos beta + cos alpha sin beta) ^(2) + (cos alpha coa beta - sin alpha sin beta) ^(2) =1.

Show that cos^(-1) ((cos alpha+cos beta)/(1+cosalpha cosbeta))=2 tan^(-1)(tan (alpha/2) tan (beta/2))

Prove that : (cos alpha + cos beta)^2 + (sin alpha + sin beta)^2 = 4 cos^2 ((alpha-beta)/(2))

Show that cos ^2 alpha + cos^2 (alpha +Beta) - 2 cos alpha cos betacos (alpha+ beta) =sin^2 beta

If ( cos x - cos alpha)/(cos x - cos beta) = ( sin^2 alpha cos beta)/(sin^2 beta cos alpha) then cos x =

If alpha+beta+gamma=pi , prove that : cos^2 alpha + cos^2 beta + cos^2 gamma+2cosalpha cosbeta cosgamma=1 .

If cos theta=(cos alpha cos beta)/(1-sin alpha sin beta), prove that one value of tan (theta/2)=(tan (alpha/2)-tan (beta/2))/(1-tan (alpha/2) tan (beta/2)).