The number of ordered pairs (α , β), where α , β belongto (-pi,pi)satisfying cos (α - β)=1 and cos (α + β)=1/e is A)0B)1C)2D)4

The first eqn is easy and will give only one solution for alpha-beta

The second one, 1/e lies between 0and 1. i.e alpha +beta lies between 0 and 90.

But sesequently, the range would be higher than that for alpha and beta separately in whichalpha +beta can lie. This eqn hence will have 4 equalities. And hence, 4 solution for the values of alpha and beta which can ssatisfy the given eqns.