tanX,tanY是方程X²+(4M+1)X+2M=0的俩根,且M≠-1／2求sin(X+Y)／cos(X-Y)

题目

tanX,tanY是方程X²+(4M+1)X+2M=0的俩根,且M≠-1／2求sin(X+Y)／cos(X-Y)

答案

sin(X+Y)／cos(X-Y)=(tanx+tany)/(1+tanxtany)
由于tanx,tany为方程X²+(4M+1)X+2M=0的俩根
所以,tanx+tany=-(4M+1),tanxtany=2M
所以sin(X+Y)／cos(X-Y)=(tanx+tany)/(1+tanxtany)=-(4M+1)/(2M+1)