The number of ordered pairs `(alpha, beta)` where `alpha, beta in (-pi, pi)` satisfying `cos (alpha-beta)=1` and `cos (alpha+beta)=1/e` is

The number of ordered pairs ( alpha, beta ) ,where alpha, beta in (-pi, pi) satisfying cos(alpha-beta) =1 "and" cos(alpha+beta) = (1)/(sqrt2) is :

The number of ordered pairs (alpha , beta ) , where alpha , beta in [0,2pi] satisfying log_(2 sec x )(beta^(2)-6beta+10)=log_(3)| cos alpha | is

If 0 lt alpha, beta lt pi and they satisfy cos alpha + cosbeta - cos(alpha + beta)=3/2

The value of 2alpha+beta(0ltalpha, beta lt (pi)/(2)) , satisfying the equation cos alpha cos beta cos (alpha+beta)=-(1)/(8) is equal to

sin alpha+sin beta=(1)/(4) and cos alpha+cos beta=(1)/(3) The value of cos(alpha+beta) is

f(alpha,beta) = cos^2(alpha)+ cos^2(alpha+beta)- 2 cosalpha cosbeta cos(alpha+beta) is

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

If sin^(4) alpha + 4 cos^(4) beta + 2 = 4sqrt(2) sin alpha cos beta, alpha beta in [0, pi] , then cos (alpha + beta) - cos (alpha - beta) is equal to -sqrt(k) . The value of k is _________.

If alpha+beta= 60^0 , prove that cos^2 alpha + cos^2 beta - cosalpha cos beta = 3/4 .

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