Help proving a trig identity?

[Jiremi]

I've been working on proving this identity for quite a while now, and I still can't seem to get it. Here's the problem:

sinx + cosx + sinxtanx + cosxcotx = secxcscx

I've tried working on both the left and the right by using every method I can think of, but I still can't prove it.
Any help will be greatly appreciated.

[stapel_eliz]

Are you sure that the right-hand side is a multiplication, and not an addition?

[Jiremi]

Yes, I'm quite sure. Although if it were addition, it would be a whole lot easier.

[stapel_eliz]

I can get the left-hand side to equal sec(x) + csc(x), and since this does not equal sec(x)*csc(x), I'm wondering if there is a typo in the exercise.

Have you tried graphing the left- and right-hand sides as functions (on a graphing calculator, for instance), and seeing if the lines match up? Because that's not what I'm getting.

[Jiremi]

I just asked my teacher, and she told me that there indeed was a typo in the worksheet. It should be sec(x) + csc(x), just like you said it might.
Thanks for the help~