Let `alpha, beta" such that "pi lt alpha-beta lt 3pi." If sin "alpha+sin beta=-21//65 cos alpha+cos beta=-27//65`, then find the value of `cos ""(alpha-beta)/(2)`.

Let alpha , beta be such pi lt alpha- beta lt 3 pi if sin alpha + sin beta = (-21)/(65) , and cos alpha Cos beta = (-27)/(65) then the value of cos ( alpha - beta)/(2) is

If cos alpha + cos beta = 1//2 and sin alpha+ sin beta = 1//3 , then

If alpha+ beta=-7 and alpha beta=10 then find the value of alpha-beta=__ .

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

If sin^4alpha+cos^4beta+2=4sinalphacosbeta,0lt=alpha,betalt=pi/2 then find the value of (sinalpha+cosbeta)dot

If alpha , beta in (0,pi/2), sin alpha =4/5 and cos ( alpha + beta) = ( -12)/(13) then sin beta is equal to

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

If cos alpha + cos beta =0 = sin alpha + sin beta , then cos 2 alpha + cos 2 beta is equal to

If alpha and beta are roots of the equatioin a cos theta + b sin theta = c , then find the value of tan (alpha + beta).