1. **State the problem:** Find the exact value of $$(\sec 30^\circ)(\cos 30^\circ)(\tan 60^\circ)(\cot 60^\circ)$$. 2. **Recall the definitions and values:** - $\sec \theta = \frac{1}{\cos \theta}$ - $\tan 60^\circ = \sqrt{3}$ - $\cot 60^\circ = \frac{1}{\tan 60^\circ} = \frac{1}{\sqrt{3}}$ - $\cos 30^\circ = \frac{\sqrt{3}}{2}$ 3. **Substitute values:** $$ (\sec 30^\circ)(\cos 30^\circ)(\tan 60^\circ)(\cot 60^\circ) = \left(\frac{1}{\cos 30^\circ}\right)(\cos 30^\circ)(\sqrt{3})\left(\frac{1}{\sqrt{3}}\right) $$ 4. **Simplify step-by-step:** - $\left(\frac{1}{\cos 30^\circ}\right)(\cos 30^\circ) = 1$ - $\sqrt{3} \times \frac{1}{\sqrt{3}} = 1$ 5. **Multiply all simplified parts:** $$1 \times 1 = 1$$ **Final answer:** $$1$$