Answer
$$\frac{\sin(s+t)}{\cos s\cos t}=\tan s+\tan t$$
We tackle the left side first to find out that this is an identity.
Work Step by Step
$$\frac{\sin(s+t)}{\cos s\cos t}=\tan s+\tan t$$
We start from the left side.
$$X=\frac{\sin(s+t)}{\cos s\cos t}$$
$\sin(s+t)$ would be expanded using the sine sum identity:
$$\sin(s+t)=\sin s\cos t+\cos s\sin t$$
So, $$X=\frac{\sin s\cos t+\cos s\sin t}{\cos s\cos t}$$
Now we separate $X$ into 2 fractions:
$$X=\frac{\sin s\cos t}{\cos s \cos t}+\frac{\cos s\sin t}{\cos s\cos t}$$
$$X=\frac{\sin s}{\cos s}+\frac{\sin t}{\cos t}$$
Here recall that $\frac{\sin\theta}{\cos\theta}=\tan\theta$.
$$X=\tan s+\tan t$$
Therefore the equation has been proved. It is an identity.
