若cos(π/3-α)=1/4,则cos(π/3+2α)=
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解决时间 2021-02-10 05:41
- 提问者网友：浮克旳回音
- 2021-02-09 13:10
若cos(π/3-α)=1/4,则cos(π/3+2α)=
最佳答案
- 五星知识达人网友：归鹤鸣
- 2021-02-09 13:30
cos(π/3-α)=1/4
cos[2(π/3-α)]=2cos^2(π/3-α)-1
=2*(1/4)^2-1
=1/8-1
=-7/8 =cos(2π/3-2a)
=cos[π-(π/3+2a)]
=-cos(π/3+2a)
∴cos(π/3+2α)=7/8
cos[2(π/3-α)]=2cos^2(π/3-α)-1
=2*(1/4)^2-1
=1/8-1
=-7/8 =cos(2π/3-2a)
=cos[π-(π/3+2a)]
=-cos(π/3+2a)
∴cos(π/3+2α)=7/8
全部回答
- 1楼网友：北方的南先生
- 2021-02-09 15:22
解：sin(π/3 -α)=sin[π/2-(π/6+α)]=cos(π/6+α)
∴cos(π/6+α)=1/4
故cos(π/3 +2α)=2cos²(π/6+α)-1=2×(1/4)²-1=－7/8
- 2楼网友：神鬼未生
- 2021-02-09 14:13
若sin(π/3-α)=1/4
那么cos(2π/3-2α)=1-2sin²a=1-2(1/4)²=7/8
所以cos(π/3+2α)=cos[π-(2π/3-2α)]=-cos(2π阀户脆鞠诒角错携氮毛/3-2α)=-7/8
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