cosx+cosy=1,则sinx+siny的范围

问题描述:

cosx+cosy=1,则sinx+siny的范围

令sinx+siny=α,给两式子都平方再相加:1+α²=2sinxsiny+2cosycosx+cos²x+sin²x+cos²y+sin²y1+α²=2sinxsiny+2cosycosx+2≤(sinX^2+sinY^2)+(CosY^2+cosX^2)+21+a^2≤(sinX^2+sinY^...