sin t/(1-cos t)- 1 + cos t /sin t = 0
Maybe you mean:
sin t (1+cos t)/[1-cos^2 t) - (1 + cos t)/sin t = 0
(1+cos t)/sin t - (1 + cos t)/sin t
which is indeed zero
sin t (1+cos t)/[1-cos^2 t) - (1 + cos t)/sin t = 0
(1+cos t)/sin t - (1 + cos t)/sin t
which is indeed zero