为什么sin2x+cos2x=2sin(2x+π/4)

为什么sin2x+cos2x=2sin(2x+π/4)
为什么sin2x+cos2x=2sin(2x+π/4)

为什么sin2x+cos2x=2sin(2x+π/4)
sin2x+cos2x=(根号下2)sin(2x+π/4)
sin2x+cos2x=(根号下2)[根号下2/2sian2x+根号下2/2cos2x]
=(根号下2)[cosπ/4sin2x+sinπ/4cos2x]
=(根号下2)sin(2x+π/4)

2sin(2x+π/4)=2(sin2xcosπ/4+sinπ/4cos2x)=√2sin2x+√2cos2x

这个题有误。把右边按照辅助角公式拆开就可以得到右边=2sin2xcosπ/4+2cos2xsinπ/4=根号2倍（sin2x+cos2x）所以原不等式应该为sin2x+cos2x=根号2*sin(2x+π/4)