sinh (x+y)=sinh x cosh y+cosh xsinh y怎么证明?
问题描述：
sinh (x+y)=sinh x cosh y+cosh xsinh y
怎么证明?
答
sin(A+B)=sinA*cosB+cosA*sinB
sinh (x+y)=sin(hx+hy)
=sin hx *cos hy +cos hx*sin hy
答
用定义带进去.sinh x*cosh y + cosh x*sinh y=[e^x-e^(-x)]/2*[e^y+e^(-y)]/2 + [e^x+e^(-x)]/2*[e^y-e^(-y)]/2=[e^(x+y)-e^(y-x)+e^(x-y)-e^(-x-y)]/4 + [e^(x+y)+e^(y-x)-e^(x-y)-e^(-x-y)]/4=[e^(x+y)-e^(-x-y)]/...