I have a formula here involving some trig and I have to simplify it in order to take the partial derivatives for the error calculation. Unfortunately, trig identities have always been my weakness.
$$n= \frac{\sin(\frac{x+y}{2})}{\sin(\frac{x}{2})}$$
The instructions were to expand it out and simplify before taking the derivatives. It was hinted at that the sum difference identity $\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)$ would be helpful.
I applied the identity and ended up with this:
$$n=\frac{\sin(\frac{x}{2})\cos(\frac{y}{2})+\cos(\frac{x}{2})\sin(\frac{y}{2})}{\sin(\frac{x}{2})}$$
I've been staring at this for much longer than I'd like to admit but cannot see how to get it in simpler terms than the original equation.