在一个直角三角形ABC中（对不起，没有图）设AB=c BC=a AC=b（c为斜边）假设∠ABC=α则sin(α)=b/c cos(α)=a/c所以sin^2(α)＋cos^2(α)=(b/c)^2+(a/c)^2又因为a^2+b^2=c^2（勾股定理）所以sin^2(α)＋cos^2(α)=(b/c)^2+(a/c)^2=(a^2+b^2)/c^2=c^2/c^2=1
