[" Let "alpha,beta" be such that "pi

If cos(alpha - beta) = 1 and cos(alpha + beta) = 1/e , then the number of ordered pairs (alpha,beta) such that alpha,beta in [-pi,pi] is :

If cos (alpha -beta) =(sqrt3)/(2) and cos (alpha + beta)=1/e, then the number of ordered pairs (alpha , beta) such that alpha, betain [-pi, pi] is

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

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

If alpha, beta be such that pi < alpha- beta < 3 pi . If sin alpha +sin beta= -21/65 and cos alpha + cos beta = -27/65 , then the value of cos frac (alpha-beta)(2) is :

Let f:[0,2] to RR be the function defined by f(x)=(3-sin (2pix)) sin (pi x-(pi)/(4)) - sin (3pi x+(pi)/(4)) If alpha,beta in [0,2] are such that {x in [0,2]: f(x) ge0}= [alpha, beta] , then the value of beta- alpha is._________

Let alpha and beta be such that pi < alpha-beta<3pi, If sinalpha+sinbeta=-(21)/(65) and cosalpha+cosbeta=-(27)/(65) , then the value of cos(alpha-beta)/2 is (a) -3/(sqrt(130)) (b) 3/(sqrt(130)) (c) 6/(25) (d) 6/(65)

If sin (120^(@) - alpha) = sin (120^(@) - beta) and 0 lt alpha,beta lt pi then all the values of alpha,beta are

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