若三角形ABC为锐角三角形,满足sinA/sinB=cos(A+B)则tanA最大值

问题描述:

若三角形ABC为锐角三角形,满足sinA/sinB=cos(A+B)则tanA最大值

做任务.......

sinA/sinB=cos(A+B)=cosAcosB-sinAsinB;sinA/cosA=sinB(cosAcosB-sinAsinB)/cosAtanA=sinB(cosB-tanAsinB)tanA=(sinBcosB)/(1+sinB^2)=sin2B/(2+2sinB^2)=sin2B/(3-cos2B)相当于圆x^2+y^2=1上面一个动点与定点(3,0...