如何得出：2+sin2x+cos2x=根号2sinsin(2x+π/4)+2

1.你最后结果写错了.2+sin2x+cos2x=2+根号2（根号2/2*sin2x+根号2/2*cos2x)
=2+根号2（cosπ/4*sin2x+sinπ/4*cos2x)
=2+根号2*sin(2x+π/4)
2.用和差化积公式（在网上可以搜到）
sin(x+π/6)+sin(x-π/6)+cosx
=2sin【（x+π/6）/2+(x-π/6)/2】cos【（x+π/6）/2-(x-π/6)/2】+cosx
=2sinxcosπ/6+cosx