1. Let $a \in\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$, then the size order of $(\cos a)^{\cos a},(\sin a)^{\cos a},(\cos a)^{\sin a}$ is
(A) $(\cos a)^{\cos a}<(\sin a)^{\cos a}<(\cos a)^{\sin a}$
(B) $(\cos a)^{\cos a}<(\cos a)^{\sin a}<(\sin a)^{\cos a}$;
(C) $(\sin a)^{\cos a}<(\cos a)^{\cos a}<(\cos a)^{\sin a}$
(D) $(\cos a)^{\sin a}<(\cos a)^{\cos a}<(\sin a)^{\cos a}$
(D)
I. Multiple Choice Question
1. 【Analysis and Solution】 $\because a \in\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$,
$$
\begin{array}{l}
\therefore 0<\cos a<\frac{\sqrt{2}}{2}<\sin a<1 . \\
\text { Therefore }(\cos a)^{\sin a}<(\cos a)^{\cos a}, \\
\therefore(\cos a)^{\cos a}<(\sin a)^{\cos a} .
\end{array}
$$