y=√2sin(2x+π／4)-1/2cos²x 化简~急用~

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/21 19:05:07

y=√2sin(2x+π／4)-1/2cos²x
=√2[sin(2x)cos(π/4)+cos(2x)sin(π/4)]-1/2cos²x
=√2[sin(2x)·√2/2+cos(2x)·√2/2]-1/2·(cos2x-1)/2
=[sin(2x)+cos(2x)]-1/4·cos2x+1/4
=sin(2x)+3/4·cos(2x)+1/4
=√[1²+(3/4)²]sin(2x+φ) （辅助角公式）
=5/4·sin(2x+φ)

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