Ask Me Help Desk - Prove that cos((pi/2-x)-y)=sin(x y)?

Please note that for some reason this site loses any "+" signs that you put in the subject header for your question. I assume what you mean is this:

$<br /> \cos((\frac {\pi} 2 -x)-y) = \sin(x+y)<br />$

This is a siimple use of the identities for $\cos (a-b)$ and $\sin (a+b)$ , and also use of $\cos (\frac {\pi} 2 - x) = \sin x$ and $\sin(\frac {\pi} 2 - x) = \cos x$ .

Alternatively if you recognize that $\cos((\frac {\pi} 2 -x)-y) = \cos(\frac {\pi} 2 -(x+y))$ and apply the identity for $\cos (a-b)$ then it comes right out.