Prove x cosx < sinx on 0 < x < pi/2

I am asked to prove that if , where the definition of is given by . I think I have a bit of the problem figured out. I reason that I can solve the whole problem if I know the derivative of is always negative, which it is if I am to trust a graphing calculator.

Once that's obtained, I think the rest follows from: , and .

So I need to show that is negative within these bounds. But I don't see how to do so, or if I need to re-consider how I'm approaching the task.