y=√2sin(2x+π／4)-1/2cos²x 化简~急用~
问题描述：
y=√2sin(2x+π／4)-1/2cos²x 化简~急用~
答
y=√2（sin2xcosπ/4+cos2xsinπ/4-1/4(cos2x+1)
=sin2x+cos2x-1/4cos2x-1/4
=sin2x-3/4cos2x-1/4
=
答
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)