函数y=(1+sinx)/(2+cosx)的值域为

题目

函数y=(1+sinx)/(2+cosx)的值域为

答案

2y+ycosx=1+sinxsinx-ycosx=2y-1√(1+y²)sin(x+θ)=2y-1则：sin(x+θ)=(2y-1)/√(1+y²)则显然有：-1≦(2y-1)/√(1+y²)≦1即：(2y-1)²/(1+y²)≦1 (2y-1)²≦y²+1 3y
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