tan(x-y)=2,tan(x+y)=3 求tan2x/tan2y
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tan(x-y)=2,tan(x+y)=3 求tan2x/tan2y
![tan(x-y)=2,tan(x+y)=3 求tan2x/tan2y](/uploads/image/z/19744407-63-7.jpg?t=tan%28x-y%29%3D2%2Ctan%28x%2By%29%3D3+%E6%B1%82tan2x%2Ftan2y)
tan2x=tan[(x+y)+(x-y)]=[tan(x+y)+tan(x-y)]/[1-tan(x+y)tan(x-y)]=(3+2)/(1-3×2)=-1
tan2y =tan[(x+y)-(x-y)]=[tan(x+y)-tan(x-y)]/[1+tan(x+y)tan(x-y)]=(3-2)/(1+3×2)=1/7
所以
tan2x/tan2y =-1/(1/7)=-7
tan2y =tan[(x+y)-(x-y)]=[tan(x+y)-tan(x-y)]/[1+tan(x+y)tan(x-y)]=(3-2)/(1+3×2)=1/7
所以
tan2x/tan2y =-1/(1/7)=-7
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