[分析] (sin A)^(sin A) < (cos A)^(cos A) for 0<A<pi/4

[snaredrum (好聽木琴)]

(sin A)^(sin A) < (cos A)^(cos A)   for 0<A<pi/4

how to prove it?

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 69.143.196.235
推 icenuclear:x1*logx1 < x2*logx2 iff 0<x1<x2
→ snaredrum:x*ln x 在(0,pi/4) 不是遞增吧... if x < 1/e  f'<0
推 math1209:我沒有什麼好辦法，我用 Lagrange Multiplier Method.