If tan `(alpha )/(2) : tan ""(beta)/(2) = 1 : sqrt3` show that ` cos beta = ( 2 cos alpha - 1 )/( 2- cos alpha ).`

If tan ""(alpha )/(2) = sqrt ({(1 -e)/( 1 +e)}) tan ""(beta)/(2), Prove that cos beta = ( cos alpha - e )/( 1 - e cos alpha ).

If 2 tan (alpha/2)=tan (beta/2), prove that cos alpha=(3+5 cos beta)/(5+3 cos beta).

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

If tan "" (alpha )/(2) and tan "" (beta)/( 2) are the roots of the equation 8x ^(2) -26x + 15 =0, then find the value of cos (alpha + beta).

If sin alpha + sin beta = a and cos alpha + cos beta = b, prove that : cos (alpha-beta) = 1/2 (a^2 + b^2 -2)

Given that sin ^(2) beta = sin alpha cos alpha, show that cos 2 beta=2 cos ^(2) ((pi)/(4) + alpha )).

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

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)

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

If alpha and beta are non-zero real number such that 2(cos beta-cos alpha)+cos alpha cos beta=1. Then which of the following is treu?