18. Find the value of
$$
\prod_{k=1}^{45} \tan (2 k-1)^{\circ}
$$
18. Ans: 1
Note that $\tan \left(90^{\circ}-\theta\right)=1 / \tan \theta$ for $0^{\circ}<\theta<90^{\circ}$ and that the product is positive. Setting $j=46-k$,
$$
\prod_{k=1}^{45} \tan (2 k-1)^{\circ}=\prod_{j=1}^{45} \tan (90-(2 j-1))^{\circ}=\frac{1}{\prod_{j=1}^{45} \tan (2 j-1)^{\circ}}=1 .
$$