#### Answer

$\frac{\sin(s+t)}{\cos s\cos t}=\tan s+\tan t$

#### Work Step by Step

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.