若sinX+cosY=2分之根号2,则cosX+sinY的范围是？
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设z=cosX+sinY
z^2+(sinX+cosY)^2
=(cos^2x+sin^2y+2cosxsiny)+(sin^2x+cos^2y+2sinxcosy)
=2+2(cosxsiny+sinxcosy)
=2+2sin(x+y)
所以，z^2+1/2=2+2sin(x+y)
z^2=3/2+2sin(x+y)
z^2≤7/2
-√14/2≤z≤√14/2
cosX+sinY的范围是:[-√14/2,√14/2]
z^2+(sinX+cosY)^2
=(cos^2x+sin^2y+2cosxsiny)+(sin^2x+cos^2y+2sinxcosy)
=2+2(cosxsiny+sinxcosy)
=2+2sin(x+y)
所以，z^2+1/2=2+2sin(x+y)
z^2=3/2+2sin(x+y)
z^2≤7/2
-√14/2≤z≤√14/2
cosX+sinY的范围是:[-√14/2,√14/2]
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