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用三角函数定义证明cosα/1-sinα=1+sinα/coaα
人气:264 ℃ 时间:2019-08-21 05:10:15
解答
设(x,y)为 α 终边上任意一点,r^2=x^2+y^2 ,r>0
sinα=y/r,cosα=x/r
左边=(x/r)/[1-(y/r)]=x/(r-y)
右边=(1+y/r)/(x/r)=(r+y)/x=(r+y)(r-y)/[x(r-y)]=(r^2-y^2)/[x(r-y)]=x^2/[x(r-y)]=x/(r-y)=左边
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