函数f(x)=lg(sin2x+√3cos2x-1)的定义域是

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函数f(x)=lg(sin2x+√3cos2x-1)的定义域是

函数f(x)=lg(sin2x+√3cos2x-1)的定义域是
函数f(x)=lg(sin2x+√3cos2x-1)的定义域是

函数f(x)=lg(sin2x+√3cos2x-1)的定义域是
2sin(2x+π/3)-1>0
sin(2x+π/3)>1/2
2kπ+π/6

sin2x+根号3cos2x-1>0,即
2sin(2x+π/3)-1>0,得
π/6+2kπ<2x+π/3<5π/6+2kπ,k∈Z,

答:
f(x)=lg(sin2x+√3cos2x-1)的定义域满足:
sin2x+√3cos2x-1>0
sin2x+√3cos2x>1
(1/2)sin2x+(√3/2)cos2x>1/2
sin(2x+π/3)>1/2
所以:2kπ+π/6<2x+π/3<2kπ+5π/6
所以:kπ-π/12所以:定义域为(kπ-π/12,kπ+π/4)k∈Z