MathDB

Let

\alpha\in(\frac{\pi}{4},\frac{\pi}{2})

, then the order of

(\cos\alpha)^{\cos\alpha},(\sin\alpha)^{\cos\alpha},(\cos\alpha)^{\sin\alpha}

\text{(A)}(\cos\alpha)^{\cos\alpha}<(\sin\alpha)^{\cos\alpha}<(\cos\alpha)^{\sin\alpha}

\text{(B)}(\cos\alpha)^{\cos\alpha}<(\cos\alpha)^{\sin\alpha}<(\sin\alpha)^{\cos\alpha}

\text{(C)}(\sin\alpha)^{\cos\alpha}<(\cos\alpha)^{\cos\alpha}<(\cos\alpha)^{\sin\alpha}

\text{(D)}(\cos\alpha)^{\sin\alpha}<(\cos\alpha)^{\cos\alpha}<(\sin\alpha)^{\cos\alpha}

Problem Statement