即證cos(π/2-cosθ)＜cos(sinθ)
　∵ -π＜π/2-1≦π/2-cosθ≦π/2+1＜π 且 -π＜-1≦sinθ≦1＜π
　∴ |sinθ|＜|π/2-cosθ| <=> cos(π/2-cosθ)＜cos(sinθ)
即證 |sinθ|＜|π/2-cosθ|
　∵ 0＜π/2-1≦π/2-cosθ
　∴|π/2-cosθ|=π/2-cosθ
即證 |sinθ|＜π/2-cosθ
　當θ€[2nπ,π+2nπ]時(其中n為整數)，|sinθ|=sinθ
　　欲證sinθ＜π/2-cosθ
　　即證sinθ+cosθ=√2 sin(θ+π/4)＜π/2
　　For all θ€[2nπ,π+2nπ]　√2 sin(θ+π/4)≦√2＜1.5＜π/2
　當θ€[π+2nπ,2π+2nπ]時(其中n為整數)，|sinθ|=-sinθ
　　欲證-sinθ＜π/2-cosθ
　　即證-sinθ+cosθ=√2 cos(θ+π/4)＜π/2
　　For all θ€[π+2nπ,2π+2nπ]　√2 cos(θ+π/4)≦√2＜1.5＜π/2

得證


參考
http://www.wretch.cc/blog/airroger1&article_id=12117587