命题q:对任意x∈R,|1+sin2x-cos2x|≤2m|cos(x-π/4)|求m的范围
问题描述：
命题q:对任意x∈R,|1+sin2x-cos2x|≤2m|cos(x-π/4)|
求m的范围
答
left:1+sin2x-cos2x=sinx^2+cosx^2+2sinxcosx-(cosx^2-sinx^2)=(sinx+cosx)^2-(cosx+sinx)(cosx-sinx)=(sinx+cosx)(sinx+cosx-cosx+sinx)right:2m(cos(x-π/4))=2m(cosxcosπ/4+sinxsinπ/4)=√2m(cosx+sinx)∵x∈R...