If π2<α<π, then √1−cosα1+cosα+√1+cosα1−cosα=
√1−cosα1+cosα+√1+cosα1−cosα
=√(1−cosα)2sin2α+√(1+cosα)2sin2α
=|cosecα−cotα|+|cosecα+cotα|
=2cosecα because sinα>0,α∈(π2,π)
If cotα+tanα=m and 1cosα−cosα=n, then