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 a "no-no" point before you hit the whole argument with the tan or cotan function.

Best of luck!

...it was early and I was full of no coffee...

P.S. Also, double-check yourself on where the Cotan function is undefined.

...it was early and I was full of no coffee...

Yep but if I use double angle formulas to expand to simplify I will end up separating the variables inside and it can' t be simplified :{

Are you sure it can't be simplified?

tan((pi/2)-y) = sin((pi/2)-y)/cos((pi/2)-y) = (sin(pi/2)*cos(y)-cos(pi/2)*sin(y))/(cos(pi/2)*sin(y)+sin(pi/2)*sin(y))

now, you use the fact that sin and cos are defined in pi/2
sin(pi/2)=1
cos(pi/2)=0

so
tan((pi/2)-y) = cos(y)/sin(y) = cot(y)

No you dropped the (pi/2 - y) for y, which makes the first and second in your equation unequal.

What do you mean, Unknown008?

Just expanded by definitions of trigonometric functions and using the identity of the sin and cos of the sum of 2 angles, and then replace some values. Didn't "drop" any part of it.

Oh, sorry, I was distracted and thought you put in sin(y)/cos(y).

Apologies :o