求公式tan(a+b)=(tana+tanb)/(1-tanatanb)的证明
问题描述:
求公式tan(a+b)=(tana+tanb)/(1-tanatanb)的证明
答
tanA+tanB
=sinA/cosA+sinB/cosB=(sinAcosB+cosAsinB)/(cosAcosB)
=sin(A+B)/(cosAcosB)=[sin(A+B)/cos(A+B)][cos(A+B)/(cosAcosB)]
=tan(A+B)[(cosAcosB-sinAsinB)/(cosAcosB)]
=tan(A+B)[1-(sinA/cosA)(sinB/cosB)]
=tan(A+B)(1-tanAtanB)