1/sin(x-120)-1/sin(x+120)=4根号3/3,求cosx
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1/sin(x-120)-1/sin(x+120)=4根号3/3,求cosx
![1/sin(x-120)-1/sin(x+120)=4根号3/3,求cosx](/uploads/image/z/5176912-40-2.jpg?t=1%2Fsin%28x-120%29-1%2Fsin%28x%2B120%29%3D4%E6%A0%B9%E5%8F%B73%2F3%2C%E6%B1%82cosx)
答案:cosx=-1 或 cosx=1/4
根据和差化积公式,
[sin(x+120°)-sin(x-120°)]/sin(x+120°)*sin(x-120°)=4根号3/3,
(2cosxsin120°)/[(cos240°-cos2x)/2]=4根号3/3,
化简:2cos2x+3cosx+1=0
2(2cos²x-1)+3cosx+1=0
所以,4cos²x+3cosx-1=0
(cosx+1)(4cosx-1)=0
所以,cosx=-1 或 cosx=1/4
根据和差化积公式,
[sin(x+120°)-sin(x-120°)]/sin(x+120°)*sin(x-120°)=4根号3/3,
(2cosxsin120°)/[(cos240°-cos2x)/2]=4根号3/3,
化简:2cos2x+3cosx+1=0
2(2cos²x-1)+3cosx+1=0
所以,4cos²x+3cosx-1=0
(cosx+1)(4cosx-1)=0
所以,cosx=-1 或 cosx=1/4
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