7・1 If $\sin \alpha \cdot \sec \alpha \sqrt{\csc ^{2} \alpha-1}=-1$. Then the range of values for $\alpha$ is
(A) First quadrant and third quadrant.
(B) Third quadrant and fourth quadrant.
(C) Second quadrant and fourth quadrant.
(D) First quadrant and fourth quadrant.
(Beijing High School Mathematics Competition, 1990)
[Solution] From $\sin \alpha \cdot \sec \alpha \cdot \sqrt{\csc ^{2} \alpha-1}=\operatorname{tg} \alpha \cdot|\operatorname{ctg} \alpha|$, then $\operatorname{tg} \alpha \cdot|\operatorname{ctg} \alpha|=-1$, we know that $\alpha$ is in the II, IV quadrants. Therefore, the answer is $(C)$.