1. **State the problem:** Simplify the expression $\tan 40^\circ - \frac{\sin 40^\circ}{\cos 40^\circ}$. 2. **Recall the formulas:** - $\tan \theta = \frac{\sin \theta}{\cos \theta}$. - The expression involves $\tan 40^\circ$ and $\frac{\sin 40^\circ}{\cos 40^\circ}$ which are equivalent. 3. **Rewrite the expression using the formula:** $$\tan 40^\circ - \frac{\sin 40^\circ}{\cos 40^\circ} = \frac{\sin 40^\circ}{\cos 40^\circ} - \frac{\sin 40^\circ}{\cos 40^\circ}$$ 4. **Simplify the expression:** $$\frac{\sin 40^\circ}{\cos 40^\circ} - \frac{\sin 40^\circ}{\cos 40^\circ} = 0$$ 5. **Conclusion:** The expression simplifies to zero.