Math Help - trig identity

1. trig identity

If $sin\theta+sin\phi=a,cos\theta+cos\phi=b$ prove that $\frac{sin\frac{(\theta+\phi)}{2}}{a}$= $\frac{\frac{(cos\theta+\phi)}{2}}{b}$= $\frac{2cos(\frac{\theta-\phi)}{2}}{a^2+b^2}$

2. Re: trig identity

Re-write a and b using these:

$\sin \theta+\sin \phi=2\sin \frac{\theta+\phi}{2}\cos \frac{\theta-\phi}{2}$
$\cos \theta+\cos \phi=2\cos \frac{\theta+\phi}{2}\cos \frac{\theta-\phi}{2}$

Then calculate each fraction.