Question

sinx+siny=1/3,求cosx+cosy的取值范围

Answer 1

（sinx+siny）^2+(cosx+cosy)^2

=2+2(sinxsiny+cosxcosy)

=2+2cos(x-y)

2cos(x-y)值域[-2,2]

（sinx+siny）^2=1/9

(cosx+cosy)^2属于[-1/9,35/9]且(cosx+cosy)^2>=0得解