已知sinx-siny=-23,cosx-cosy=23且x,y为锐角,则tan(x-y)= ___ .
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已知sinx-siny=-
2 |
3 |
![已知sinx-siny=-23,cosx-cosy=23且x,y为锐角,则tan(x-y)= ___ .](/uploads/image/z/5072687-71-7.jpg?t=%E5%B7%B2%E7%9F%A5sinx-siny%3D-23%EF%BC%8Ccosx-cosy%3D23%E4%B8%94x%EF%BC%8Cy%E4%B8%BA%E9%94%90%E8%A7%92%EF%BC%8C%E5%88%99tan%EF%BC%88x-y%EF%BC%89%3D+___+%EF%BC%8E)
∵sinx-siny=-
2
3,cosx-cosy=
2
3,
两式平方相加得:cos(x-y)=
5
9,
∵x、y为锐角,sinx-siny<0,
∴x<y,
∴sin(x-y)=-
1-cos2(x-y)=-
2
14
9,
∴tan(x-y)=
sin(x-y)
cos(x-y)=
-
2
14
9
5
9=-
2
14
5.
故答案为:-
2
14
5.
2
3,cosx-cosy=
2
3,
两式平方相加得:cos(x-y)=
5
9,
∵x、y为锐角,sinx-siny<0,
∴x<y,
∴sin(x-y)=-
1-cos2(x-y)=-
2
14
9,
∴tan(x-y)=
sin(x-y)
cos(x-y)=
-
2
14
9
5
9=-
2
14
5.
故答案为:-
2
14
5.
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