Verify the trigonometric identity:
(cos Ɵ - (sin Ɵ - 1))/(cos Ɵ + (sin Ɵ - 1)) = (1+cos Ɵ)/(sin Ɵ)
(cos-(sin-1))/(cos+(sin-1))
(cos-(sin-1))^2/(cos+(sin-1))(cos-(sin-1))
cos^2 - 2cos(sin-1) + (sin-1)^2
-------------------------------------
cos^2 - (sin-1)^2
cos^2 - 2sin*cos + 2cos + sin^2 - 2sin + 1
-----------------------------------------
cos^2 - sin^2 + 2sin - 1
2cos - 2sin*cos - 2sin + 2
-----------------------
2sin^2 - 2sin
(cos-sin*cos-sin+1)/(sin^2-sin-1)
(cos+1)(1-sin)
---------------------
sin(1-sin)
(cos+1)/sin