求函数y=(√[sin x-((√3)⼀2)])+lg[√2-(2cos x)]的定义域

写出详细过程
2025-06-21 15:25:54
推荐回答(1个)
回答1:

根号下大于等于0,真数大于0

所以sinx>=√3/2=sin(2kπ+π/3)=sin(2kπ+2π/3)
所以2kπ+π/3<=x<=2kπ+2π/3

√2-2cosx>0
cosx<√2/2=cos(2kπ+π/4)=cos(2kπ+7π/4)
所以2kπ+π/4
两者取交集
所以定义域[2kπ+π/3,2kπ+2π/3]