Question

sinx+siny=2分之根号2求cosx+cosy的范围

Answer 1

设t=cosx+cosy.又(√2)/2=sinx+siny.两式平方后相加得,cos(x-y)=(2t^2-3)/4.由-1≤cos(x-y)≤1,===>-1≤(2t^2-3)/4≤1.===>0≤t^2≤7/3.===>-(√21)/3≤t≤(√21)/3.===>-(√21)/3≤cosx+cosy≤(√21)/3.