0≤x≤45°
0≤2x≤90°
60°≤2x+60°≤150°
-√3/2≤cos(2x+60°)≤1/2
-√3≤2cos(2x+60°)≤1
4-√3≤4+2cos(2x+60°)≤5
y=3sin^2 x -2√3sinx*cos x +5cos^2x
=3(sin^2 x+cos^2x) -√3*sin(2x) +2cos^2x
=3-sin(2x)*sin60°/cos60°+1+cos(2x)
=4+cos(2x)-sin(2x)*sin60°/cos60°
=4+[cos(2x)*cos60°-sin(2x)*sin60°]/cos60°
=4+2cos(2x+60°)
y=3sin^2 x -2√3sinx*cos x +5cos^2x的值域:4-√3≤y≤5