答：
1）
5cos(2x-y)+7cosy=0
5cos[(x-y)+x]+7cos[x-(x-y)]=0
5cos(x-y)cosx-5sin(x-y)sinx +7cosxcos(x-y)+7sinxsin(x-y)=0
所以：
12cos(x-y)cosx+2sin(x-y)sinx=0
所以：sin(x-y)sinx=-6cos(x-y)cosx
所以：tan(x-y)tanx=-6
2）
y=sin²（x+π/4)-sin²（x-π/4),x∈（π/6,π/3）值域
=(1/2)*[1-cos(2x+π/2) ]- (1/2)*[1-cos(2x-π/2)]
=(1/2) * [cos(2x-π/2)-cos(2x+π/2) ]
=(1/2)* (sin2x+sin2x)
=sin2x
π/6