If `alpha and beta` are angles such that `alpha+beta=(2pi)/3`, then number of integers in range of `( sinalpha – sinbeta+ 4cos alpha cos beta)`

If alpha and beta are angles such that alpha+beta=(2 pi)/(3) then number of integers in range of (sin alpha sin beta+4cos alpha cos beta)

sin alpha=sinbeta, cos alpha=cos beta then

If cos alpha+cos beta=0=sin alpha+sinbeta, then cos2alpha+cos 2beta=

If alpha , beta are complementary angles , sin alpha = 3//5 , then sin alpha cos beta - cos alpha sin beta =

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 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 alpha,beta are complementary angles, sin alpha=(4)/(5), then sin alpha cos beta+cos alpha sin beta=

If alpha,beta are complementary angles and sin alpha = (3)/(5) , then sin alpha cos beta - cos alpha sin beta =