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

If 2\ t a nalpha=3t a nbeta, prove that tan(alpha-beta)=(sin2beta)/(5-cos2beta)

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

If cos alpha=4/5 and cos beta =5/13, prove that cos (alpha-beta)/2=28/65.

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 sin alpha=4/5 and cos beta =5/13, prove that cos ((alpha-beta)/2)=8/sqrt 65.

If 0 lt alpha, beta lt pi and they satisfy cos alpha + cosbeta - cos(alpha + beta)=3/2

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

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

Find the value of sin (alpha + beta) , cos (alpha + beta) , and tan (alpha + beta), given sin alpha = (3)/(5) , cos beta = (5)/(13), alpha and beta in Quadrant I.