cos(a-b)=-2分之1,sin(a+b)=2分之根3,a -b∈(π,2分之3π),a+b∈(0,2分之π),则cos2a的值
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![cos(a-b)=-2分之1,sin(a+b)=2分之根3,a -b∈(π,2分之3π),a+b∈(0,2分之π),则cos2a的值](/uploads/image/z/5170034-2-4.jpg?t=cos%28a-b%29%3D-2%E5%88%86%E4%B9%8B1%2Csin%28a%2Bb%29%3D2%E5%88%86%E4%B9%8B%E6%A0%B93%2Ca+-b%E2%88%88%28%CF%80%2C2%E5%88%86%E4%B9%8B3%CF%80%29%2Ca%2Bb%E2%88%88%280%2C2%E5%88%86%E4%B9%8B%CF%80%29%2C%E5%88%99cos2a%E7%9A%84%E5%80%BC)
cos(a-b)=-2分之1,sin(a+b)=2分之根3,a -b∈(π,2分之3π),a+b∈(0,2分之π),则cos2a的值
cos(a-b)=-2分之1,sin(a+b)=2分之根3,a -b∈(π,2分之3π),a+b∈(0,2分之π),则cos2a的值
cos(a-b)=-2分之1,sin(a+b)=2分之根3,a -b∈(π,2分之3π),a+b∈(0,2分之π),则cos2a的值
∵cos(a-b)=-1/2且a -b∈(π,3/2π)
∴a-b=4/3π; ……①
又∵sin(a+b)=2分之根3且a+b∈(0,π/2)
∴a+b=π/3; ……②
联立①②可得到2a=5/3π,
∴cos2a=1/2.
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