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?