tan theta/sec theta-1 = sec theta + 1/tan theta
tan/(sec - 1) =
tan( sec + 1) tan( sec + 1)
--------------------------- = ----------------------- = ( sec^2 - 1 = tan^2 )
(sec - 1)( sec + 1) sec^2 - 1
tan( sec + 1) sec + 1 1/cos + 1
------------------- = ---------------- = ---------------- =
tan ^2 tan sin/cos
1/cos + cos/cos ( 1 + cos)/cos 1 + cos
---------------------- = -------------------- = ---------------- =
sin/cos sin/cos sin
1/sin + cos/sin - sec + cot = cot = 1/tan
sec + 1/tan