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 (-pi, pi) satisfying cos(alpha-beta) =1 "and" cos(alpha+beta) = (1)/(sqrt2) is :

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

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

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

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

Find the values of alpha and beta[ 0 lt alpha, beta lt (pi)/(2)] satisfying the equation cos alpha cos beta cos (alpha+ beta)=-(1)/(8)