y=(sinx+cosx)^2+2(cosx)^2
=(sinx)^2+2sinxcosx+(cosx)^2+2(cosx)^2
=1+sin2x+2(cosx)^2
=2+sin2x+2(cosx)^2-1
=2+sin2x+cos2x
=2+√2(√2/2sin2x+√2/2cos2x)
=2+√2(sin2xcosπ/4+sinπ/4cos2x)
=2+√2sin(2x+π/4)
1、递减区间为：[kπ＋π/8,kπ＋5π/8],k是整数
2、最大值为2＋√2,当x＝kπ＋π/8取得最大值
最小值为2－√2,当x＝kπ＋5π/8取得最小值