1. To clarify your question, it seems you are asking about why the last function or expression involves the tangent function (tan). 2. The tangent function typically appears as the ratio of sine and cosine: $$\tan x = \frac{\sin x}{\cos x}$$. 3. If in a problem the expression simplifies or transforms to $$\tan x$$, it's often because the sine and cosine terms divide out. 4. Without the exact problem, a general explanation is that when you encounter a ratio of sine to cosine, the result is the tangent function. 5. If you provide the exact problem or the last expression, I can explain precisely why tan appears.