Question

How to prove !?

Prove `tan(A - B)` = `(tanA-tanB)/(1+tanAtanB)`

Answer 1

`RHS=(tanA-tanB)/(1+tanA*tanB)`

`=(sinA/cosA-sinB/cosB)/(1+(sinAsinB)/(cosA*cosB))`

`=((sinA*cosB-cosA*sinB)/(cosA*cosB))/((cosAcosB+sinAsinB)/(cosA*cosB))`

`=sin(A-B)/cos(A-B)=tan(A-B)=LHS`