已知sin(X+Y)=2/3,sin(X-Y)=1/5,求(tanX)/(tanY)的值
问题描述:
已知sin(X+Y)=2/3,sin(X-Y)=1/5,求(tanX)/(tanY)的值
答
sinxcosy=2/3+1/5=13/15
cosxsiny=2/3-1/5=7/15
除一下 13/7
答
(tanX)/(tanY)=(sinX/cosX)/(sinY/cosY)=(sinXcosY)/(cosXsinY)又sinXcosY=(1/2)[sin(X+Y)+sin(X-Y)]=(1/2)[(2/3)+(1/5)]=13/30cosXsinY=(1/2)[sin(X+Y)-sin(X-Y)]=(1/2)[(2/3)-(1/5)]=7/30代入原式,得(ta...