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fx=cos(三分之四派-2x)+2cos的平方x化解
题目详情
fx=cos(三分之四派-2x)+2cos的平方x化解
▼优质解答
答案和解析
化简:f(x)=cos(4π/3-2x)+2cos²x
f(x)=cos[π+(π/3-2x)]+1+cos2x=-cos[(π/3)-2x]+cos2x+1
=-[cos(π/3)cos2x+sin(π/3)sin2x]+cos2x+1
=-(1/2)cos2x-(√3/2)sin2x+cos2x+1
=(1/2)cos2x-(√3/2)sin2x+1
=cos2xcos(π/3)-sin2xsin(π/3)+1
=cos[2x+(π/3)]+1
f(x)=cos[π+(π/3-2x)]+1+cos2x=-cos[(π/3)-2x]+cos2x+1
=-[cos(π/3)cos2x+sin(π/3)sin2x]+cos2x+1
=-(1/2)cos2x-(√3/2)sin2x+cos2x+1
=(1/2)cos2x-(√3/2)sin2x+1
=cos2xcos(π/3)-sin2xsin(π/3)+1
=cos[2x+(π/3)]+1
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