已知1/(sin(120-x))+1/(sin(120+x))=√3,求cosx的值

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已知1/(sin(120-x))+1/(sin(120+x))=√3,求cosx的值已知1/(sin(120-x))+1/(sin(120+x))=√3,求cosx的值已知1/(sin(120-x))

已知1/(sin(120-x))+1/(sin(120+x))=√3,求cosx的值
已知1/(sin(120-x))+1/(sin(120+x))=√3,求cosx的值

已知1/(sin(120-x))+1/(sin(120+x))=√3,求cosx的值
√3
=1/sin(120-x)+1/sin(120+x)
=[sin(120-x)+sin(120+x)]/sin(120-x)sin(120+x)
=2sin120cosx/(-1/2(cos240-cos2x))
=2√3cosx/(cos2x+1/2)
cos2x+1/2=2cosx
2cos^2x-1/2=2cosx
4cos^2x-4cosx-1=0
cosx=(1±√2)/2
因为:cosx∈ [-1,1]
所以,cosx=(1-√2)/2