Recall,
tan# = Sin#/Cos#
1 - Sin^2# = Cos^2#
Looking at step 1 and 2,
1 - Sin# is not equal to Cos#. Thus, (1 - Cos#)/Cos# is not equal to Cos#/Cos#
Thus, there is a mistake between step 1 and step 2
Looking at step 3 and step 4, (Cos# + Sn#)/Cos# is same as Cos#/Cos# + Sin#/Cos#
This would give us
1 + tan#
But what they got in step 4 is 1/Cos#
This is wrong
Thus, there is a mistake between step 3 and step 4