已知函数y=(sinx+cosx)^2+2cos^2x（1）当y取的最大值时,求自变量X的取值集合（2）该函数图像可由y=sinx(x属于R）的图像经过怎样的变换得到的?麻烦详细过程
解析：y=(sinx+cosx)^2+2cos^2x=sin2x+cos2x+2=√2sin(2x+π//4)+2
2x+π//4=2kπ+π/2==>x=kπ+π/8
当y取的最大值时,求自变量X的取值集合x=kπ+π/8
由y=sinx==>y=√2sin(2x+π//4)+2
(1)将Y坐标伸长√2倍,得y=√2sinx
(2)y=√2sinx水平左移π//4个单位,得y=√2sin(x+π//4)
(3)将X坐标缩小到原来的1/2,得y=√2sin(2x+π//4)
(4)将y=√2sin(2x+π//4)图像上移2个单位,得y=√2sin(2x+π//4)+2图像.