944

求值 ${\displaystyle {\displaystyle \frac{2\cos {40}^{\circ }+\cos {80}^{\circ }}{\sin {80}^{\circ }}}}$.

注意到$$\begin{array}{r}\text{原式}=\frac{2\cos ({30}^{\circ }+{10}^{\circ })+\sin {10}^{\circ }}{\cos {10}^{\circ }}=\frac{\sqrt{3}\cos {10}^{\circ }}{\cos {10}^{\circ }}=\sqrt{3}.\end{array}$$