sin2x+cos2x+2=根号2倍的sin(2x+π/4)+2怎么出来的,

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sin2x+cos2x+2=根号2倍的sin(2x+π/4)+2怎么出来的,
sin2x+cos2x+2=根号2倍的sin(2x+π/4)+2怎么出来的,

sin2x+cos2x+2=根号2倍的sin(2x+π/4)+2怎么出来的,
sin(2x)+cos(2x)+2
=√2[(√2/2)sin(2x)+(√2/2)cos(2x)]+2
=√2[sin(2x)cos(π/4)+cos(2x)sin(π/4)]+2
=√2sin(2x+π/4)+2