1-cos2x+sin2x为什么变成--根号2sin(2x-π/4)+1

问题描述:

1-cos2x+sin2x为什么变成--根号2sin(2x-π/4)+1

用辅助角公式可以得到的
sin2x-cos2x+1
=√2((√2/2)sin2x-(√2/2)cos2x)+1
=√2(sin2xcos(π/4)-cos2xsin(π/4))+1
=√2sin(2x-π/4)+1