If π<θ<2π, then √1+cosθ1−cosθ, is equal to
cosecθ+cotθ
cosecθ−cotθ
−cosecθ+cotθ
−cosecθ−cotθ
√1+cosθ1−cosθ
=√(1+cosθ)(1+cosθ)(1−cosθ)(1+cosθ)
=√(1+cosθ)21−cos2θ
=√(1+cosθ)2sin2θ
=(1+cosθ)−sinθ
[as, π<2π, so sinθ will be negative]
=−(cosecθ+cotθ)
=−cosecθ−cotθ
If a=π3e,b=3πe and c=e3π, then