证明命题错误最简单了,只要找一个反例,就可以了.令A=π,B=3π/2sin(A+B)=sin(π+3π/2)=sin(2π+π/2)=sin(π/2)=1sinA+sinB=sinπ+sin(3π/2)=0-1=-1sin(A+B)>sinA+sinB,因此命题Sin(A+B)≤SinA+SinB是错误命题....