$$
6 \cdot 40 \quad \lg \left(\tan 1^{\circ}\right)+\lg \left(\tan 2^{\circ}\right)+\lg \left(\tan 3^{\circ}\right)+\cdots+\lg \left(\tan 88^{\circ}\right)+\lg \left(\tan 89^{\circ}\right)
$$

The value is
(A) 0.
(B) $\frac{1}{2} \lg \frac{\sqrt{3}}{2}$.
(C) $\frac{1}{2} \lg 2$.
(D) 1.
(E) None of the above.
(38th American High School Mathematics Examination, 1987)
［Solution］From the given problem and properties of logarithms, we have
$$
\begin{aligned}
\text { Original expression } & =\lg \left(\tan 1^{\circ} \cdot \tan 2^{\circ} \cdot \tan 3^{\circ} \cdots \cdot \tan 88^{\circ} \cdot \tan 89^{\circ}\right) \\
& =\lg \left[\left(\tan 1^{\circ} \cdot \tan 89^{\circ}\right)\left(\tan 2^{\circ} \cdot \tan 88^{\circ}\right) \cdots \cdot\left(\tan 44^{\circ} \cdot \tan 46^{\circ}\right) \cdot \tan 45^{\circ}\right] \\
& =\lg (1 \cdot 1 \cdot \cdots \cdot 1 \cdot 1)=\lg 1=0 .
\end{aligned}
$$

Therefore, the answer is $(A)$.