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\ a n d\ cosalpha+cosbeta=b , show that : cos(alpha+beta)=(b^2-a^2)/(b^2+a^2)

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+cosbeta=b then tan((alpha-beta)/2) is equal to

If sin alpha sin beta - cos alpha cos beta + 1=0, then the value of 1+cot alpha tan beta is

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

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)

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

If alpha, beta are the roots of the equation a cos theta + b sin theta = c , then prove that cos(alpha + beta) = (a^2 - b^2)/(a^2+b^2) .

Prove that if: (sin(x-alpha))/(sin(x-beta)) =a/b and cos(x-alpha)/(cos(x-beta)) =A/B and a+b!=0 then cos(alpha-beta) = (aA+bB)/(aB+bA)