若函数f(x)=2*a*sin(2*x+b)值域为[-2,2]在区间[-5*π/12,π/12]上是单调递减函数则常数a,b的值是多少

因为值域为[-2,2] 所以a=1或-1
因为T=2π/2=π
[-5*π/12,π/12]为半个周期
所以x=-5*π/12 f(x)=2
x=π/12 f(x)=-2
x=-5*π/12 代入 -5π/6+b=2kπ+π/2 b=2kπ+4π/3