Question: simplify csc² x + cot² x
multiple choice answers are csc x, sec x, cot x, 0 , or 1

I tried:

1) csc² x + cot²x
2) 1 + cot² x + cot²x {since csc²x = 1 + cot²x}
3) 1 + 2cot²x

or

1) csc² x + cot²x
2) csc² x + csc²x - 1 {since cot²x = csc²x -1}
3) 2csc²x - 1

and got stuck from there. What do I do next?

Give this a spin... run your proposed expression through a graphing utility, and see if its "profile" resembles any of the allowable answers.

Then see what csc^2x \ - \ cot^2x looks like on the ol' grapher. Is it possible that the question calls for a minus sign in there?

And on an unrelated note, maybe next year for our Panthers?

Well, what I suggest here (I got the answer) is to continue with your second attempt.

Convert csc into sin and make everything in one fraction.

The trick here is to change the '2' into cos and sin.

Go on, substitute 2 by 1+1 and then substitute a '1' by the pythaoras identity.

This should give you the answer. Post what you did! :)