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Am I mistaken but a question such as expand and simplify:
tan((pi/2)-y) and cot((3pi/2)+x) can't be done as tan of pi/2 and 3pi/2 are undefined? I got these questions out of a maths book with no solutions, could someone please verify this. Thanks in advance.
Your instincts about the non-existence of the tan and cotan functions at certain argument values is pointing you in the right direction, and you'll be fine when you take it one step further.
Note that you've got a variable "inside" the argument in each case. Depending on what the variable's value is, it might move the whole argument off of a "no-no" point before you hit the whole argument with the tan or cotan function.