单调区间 (1 17:3:55)求函数y=sinxcosx ÷(1+sinx-cosx)的单调区间
问题描述：
单调区间 (1 17:3:55)
求函数y=sinxcosx ÷(1+sinx-cosx)的单调区间
答
sinxcosx/(1+sinx-cosx)
=2sin(x/2)cos(x/2)cosx/(2sin^2(x/2)+2sin(x/2)cos(x/2))
=cos(x/2)cosx/(sin(x/2)+cos(x/2))
=cos(x/2){cos^2(x/2)-sin^2(x/2)}/(sin(x/2)+cos(x/2))=
cos(x/2)[cos(x/2)-sin(x/2)]
=(1+cosx)/2-sinx/2
=二分之根号2 cos(x+π/4)+1/2
单调区间会了吧,自己做一下吧.