求Y=sin²X+sinX+cosX+2 （X∈R）值域

y=sin²x+sinx+cosx+2=(1-cos2x)/2+√2sin(x+л/4)+2=(1/2)*sin(2x+л/2)+ √2*sin(x+л/4)+5/2；=(1/2)*sin(2θ)+ √2*sin(θ)+5/2；θ=x+л/4；求导得：y’=cos(2θ)+ √2*cosθ=0；2cos²θ+ √2*cosθ-1...