1. (tan u - cot u) / (tan u + cot u) is an identity.
(tan u - cot u) / (tan u + cot u)
= [(sin u/cos u) - (cos u/sin u)] / [(sin u/cos u) + (cos u/sin u)]
= (sinē u - cosē u) / (sinē u + cosē u)
= sinē u - cosē u
is there any other mid steps that would be good to include?