证明：sh(x+y)=shxchy+chxshy

很简单的
右=(e^x-e^-x)(e^y+e^-y)/4+(e^x+e^-x)(e^y-e^-y)/4
=[e^(x+y)+e^(x-y)-e^(y-x)-e^(-x-y)]/4
+[e^(x+y)-e^(x-y)+e^(y-x)-e^(-x-y)]/4
=[e^(x+y)-e^(x-y)]/2
=sh(x+y)
=左边
证毕。

sh(x+y)
=[e^(x+y)-e^(-x-y)]/2
=e^xe^y/2-e^(-x)e^(-y)/2
=[e^x-e^(-x)]/2*[e^y+e^(-y)]/2+[e^x+e^(-y)]/2*[e^y-e^(-y)]/2
=shxchy+chxshy