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