9.20 If $\alpha$ is an acute angle, and the algebraic expressions are $P=\log _{\sin \alpha}\left(\sin 50^{\circ}+\cos 50^{\circ}\right), Q=$ $\log _{\sin \alpha}\left(\sin 65^{\circ}+\cos 65^{\circ}\right)$, then the relationship between $P$ and $Q$ is
(A) $P<Q$.
(B) $P>Q$.
(C) $P=Q$.
(D) Uncertain.
(China Sichuan Province High School Mathematics Competition, 1990)
$$
\begin{array}{l}
\text { Given } 0<\sin 110^{\circ}, \\
\therefore & \sin 50^{\circ}+\cos 50^{\circ}>\sin 65^{\circ}+\cos 65^{\circ} .
\end{array}
$$

Therefore, the correct choice is $(A)$.