a) y= (2-[TEX]sqrt3[/TEX] ) sin2x + cos 2x
b) y=[TEX] (sinx - cosx)^2[/TEX]+ 2cos2x + 3sinxcosx (2)
b/
[TEX](2) \Leftrightarrow 1-2sinxcosx + 2cos2x + 3sinxcosx[/TEX]
[TEX] = 2cos2x + sinxcosx + 1[/TEX]
[TEX]= 2cos2x + \frac{1}{2} sin2x +1[/TEX]
[TEX]\sqrt{a^2+b^2} = \frac{\sqrt{5}}{2}[/TEX]
[TEX](2) \Leftrightarrow \frac{\sqrt{5}}{2} ( \frac{2\sqrt{5}}{5}cos2x + \frac{\sqrt{5}}{5}sin2x +1[/TEX]
[TEX]= \frac{\sqrt{5}}{2} cos(2x-a)+1[/TEX]
[TEX]Max y/R = \frac{\sqrt{5}}{2} +1[/TEX]
[TEX]Min y/R = -\frac{\sqrt{5}}{2} +1[/TEX]