## Precalculus (6th Edition)

$\frac{\sin(s+t)}{\cos s\cos t}=\tan s+\tan t$
Start with the left side: $\frac{\sin(s+t)}{\cos s\cos t}$ Expand using the addition formula for sine: $=\frac{\sin s\cos t+\cos s\sin t}{\cos s\cos t}$ Break it into two fractions and simplify: $=\frac{\sin s\cos t}{\cos s\cos t}+\frac{\cos s\sin t}{\cos s\cos t}$ $=\frac{\sin s}{\cos s}+\frac{\sin t}{\cos t}$ $=\tan s+\tan t$ Since this equals the right side, the identity has been proven.