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

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

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

If sin (theta + alpha ) = cos ( theta + alpha), prove that tan theta =(1- tan alpha )/(1 + tan alpha )

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= 60^0 , prove that cos^2 alpha + cos^2 beta - cosalpha cos beta = 3/4 .

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 tan beta = 3 tan alpha, prove that tan (alpha + beta) = (2sin 2beta)/(1+cos 2beta)

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-t a n alpha/2 tan beta/2).

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

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