函数y=2sin(π/3-2x)的单调减区间是______

因为y=sinx的单调减区间为
[π/2+2kπ,3π/2+2kπ],k为任意整数，

所以函数y=2sin(π/3-2x)的单调减区间
为
π/2+2kπ<=π/3-2x<=3π/2+2kπ
π/6+2kπ<=-2x<=7π/6+2kπ
π/12+kπ<=-x<=7π/12+kπ
-7π/12-kπ<=x<=-π/12-kπ
即单调减区间为
[-7π/12-kπ,-π/12-kπ],k为任意整数。

y=2sin(π/3-2x)=-2sin(2x-π/3)
要求函数y的单调减区间，即求y=2sin(2x-π/3)的单调增区间
函数y=sinx的单调增区间是π/2+2kπ<x<3π/2+2kπ,
即π/2+2kπ<2x-π/3<3π/2+2kπ
解上面的不等式即可

解这个方程就行啦
2kπ+π/2<=π/3-2x<=2kπ+3π/2