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

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

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

sin alpha+sin beta=(1)/(4) and cos alpha+cos beta=(1)/(3) The value of cos(alpha+beta) is

sin alpha+sinbeta=(1)/(4) and cos alpha+cos beta=(1)/(3) the value of sin(alpha+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 sin alpha + sin beta=a and cos alpha+cosbeta=b then tan((alpha-beta)/2) is equal to

sin alpha+ sinbeta=(1)/(4) and cos alpha+cos beta=(1)/(3) The value of tan (alpha+beta) is

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