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

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

If cos alpha+ cos beta =1/3 and sin alpha+sin beta=1/4 prove that cos[(alpha-beta)/2] =+-(5/24)

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

If sin alpha+sin beta=a and cos alpha-cos beta=b then tan((alpha-beta)/2) is equal to-

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

Let alpha, beta be such that pi lt alpha-betalt3pi if sin alpha+sinbeta = -21/65 and cos alpha+cos beta = -27/65 , then the value of cos(alpha-beta)/(2) is

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

If cos alpha = (3)/(5) , cos beta = (4)/(5) , find the value of cos ""(( alpha - beta)/( 2)), assuming alpha and beta to be acute angles.

If cos alpha + cos beta + cos gamma = 0 and also sin alpha + sin beta + sin gamma= 0, then prove that: cos 3 alpha + cos 3beta + cos 3gamma = 3 cos (alpha + beta + gamma)

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)