考虑直角三角形ABC,=(a/c)^2+(b/c)^2=(a^2+b^2)/c^2=c^2/c^2=1tanα=a/b=(a/c)/(b/c)=sinα/cosα 没懂因为sinα=a/ccosα=b/c所以sin²α+cos²α=(a/c)²+(b/c)²=a²/c²+b²/c²=(a²+b²)/c²由勾股定理c²=a²+²，故sin²α+cos²α=(a²+b²)/c²=c²/c²=1 sinα/cosα=(a/c)/(b/c)=a/btanα=a/b所以tanα=sinα/cosα