求函数f(x)=Sin^2x+2SinCosx+3Cos^2x的值域
问题描述：
求函数f(x)=Sin^2x+2SinCosx+3Cos^2x的值域
答
f(x)=Sin^2x+2SinCosx+3Cos^2x
=(sin^2 x+cos^2 x)+2sinxcosx+2cos^2 x
=1+sin2x+1+cos2x
= √2 sin(2x+ π/4 )+2
所以f(x)的值域是[2-√2,2+√2]