∵$$\alpha \in \left( \frac{ \pi }{4}，\frac{ \pi }{2} \right)$$，  ∴ $$0 ~\textless{} ~\cos \alpha ~~\textless{} ~\frac{\sqrt{2}}{2} ~\textless{} ~\sin \alpha ~~\textless{} ~1$$．  故 $$\cos \alpha {{}^{\sin \alpha }} ~\textless{} ~\cos \alpha {{}^{\cos \alpha }}$$．  ∴ $$\cos \alpha {{}^{\cos \alpha }} ~\textless{} ~{{(\sin \alpha )}^{\cos \alpha }}$$． 
设$$\alpha \in \left( \frac{ \pi }{4}，\frac{ \pi }{2} \right)$$，则$${{\left( \cos \alpha \right)}^{\cos \alpha }}$$，$${{\left( \sin \alpha \right)}^{\cos \alpha }}$$，$${{\left( \cos \alpha \right)}^{\sin \alpha }}$$的大小顺序是（~ ~ ）．

  - $${{\left( \cos \alpha \right)}^{\cos \alpha }} ~\textless{} ~{{\left( \sin \alpha \right)}^{\cos \alpha }} ~\textless{} ~{{\left( \cos \alpha \right)}^{\sin \alpha }}$$； 
  - $${{\left( \cos \alpha \right)}^{\cos \alpha }} ~\textless{} ~{{\left( \cos \alpha \right)}^{\sin \alpha }} ~\textless{} ~{{\left( \sin \alpha \right)}^{\cos \alpha }}$$； 
  - $${{\left( \sin \alpha \right)}^{\cos \alpha }} ~\textless{} ~{{\left( \cos \alpha \right)}^{\cos \alpha }} ~\textless{} ~{{\left( \cos \alpha \right)}^{\sin \alpha }}$$； 
  - $${{\left( \cos \alpha \right)}^{\sin \alpha }} ~\textless{} ~{{\left( \cos \alpha \right)}^{\cos \alpha }} ~\textless{} ~{{\left( \sin \alpha \right)}^{\cos \alpha }}$$． 