" If "cos alpha=3/5&cos beta=5/13" and "alpha,beta in(0,pi/2)," value of "sin^(2)((alpha-beta)/(2))" is? "

If cos alpha=3/5 and cos beta = 5/13 and alpha , beta are acute angles , then prove that cos^(2)((alpha+beta)/2)=16/65

Let alpha,beta be such that pi lt alpha-beta lt3 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+beta)=(3)/(5) sin(alpha-beta)=(5)/(13) and 0< alpha, beta < (pi)/(4) then tan(2 alpha) is equal to

If cos alpha + cos beta = 0 = sin alpha + sin beta, then value of cos 2 alpha + cos 2 beta is

if cos alpha=(11)/(61) and sin beta=(4)/(5), find the values of sin^(2)((alpha-beta)/(2)) and cos^(2)((alpha+beta)/(2))

If sin alpha=(3)/(5) and cos beta=(9)/(41) find the value of sin(alpha-beta) and cos(alpha+beta)

If cos alpha =(3)/(5) and cos beta =(5)/(13) and alpha, beta are acute angles, then prove that (a) sin ^(2)((alpha-beta)/(2))=(1)/(65) and (b) cos ^(2)((alpha+beta)/(2))=(16)/(65)

Let alpha, beta be such that it pi < alpha - beta <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