“函数f(x)=1+sinx/2+cosx的值域为”

2025-06-21 01:20:47
推荐回答(1个)
回答1:

  f(x)=(1+sinx)/(2+cosx)的值域为??

  • 解析:

  y=(1+sinx)/(2+cosx)

  2y+ycosx=1+sinx

  sinx-ycosx=2y-1

  √(1+y²)sin(x+φ)=2y-1

  sin(x+φ)=(2y-1)/√(1+y²)

  |(2y-1)/√(1+y²)|≥1

  解得值域