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

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=

If cos alpha=(2cos beta-1)/(2-cos beta) then tan (alpha/2) is equal to

If alpha+beta=pi/4 then (1+tan alpha)(1+tan beta)=

Show that (sin (alpha + beta))/( sin (alpha + beta)) = 2, given that tan alpha = 2 tan beta.

(1+tan alpha tan beta)^2 + (tan alpha - tan beta)^2 =

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

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)).

If the eccentric angles of the extremities of a focal chord of an ellipse x^2/a^2 + y^2/b^2 = 1 are alpha and beta , then (A) e = (cos alpha + cos beta)/(cos (alpha + beta)) (B) e= (sin alpha + sin beta)/(sin(alpha + beta)) (C) cos((alpha-beta)/(2)) = e cos ((alpha + beta)/(2)) (D) tan alpha/2.tan beta/2 = (e-1)/(e+1)