(tanx / (1 - cot x)) + (cotx/(1-tanx)) = tanx + cotx + 1
So far I have gotten these:

(tanx - tanx^2 + cotx - cotx^2)/(1-tanx+1-cotx)

divide top and bottom i get:

tan(2 - 2tan) + cot(2 - 2cot)

again, divide by 2

tan + cot - tan^2 - cot^2