Prove that (sin(A+B))/(cos(A-B)) = (tan A-tan B)/(1+tan A tan B)?

2 Answers
Apr 12, 2018

(tanA-tanB)/(1+tanAtanB)=tan(A-B)=sin(A-B)/cos(A-B).

Check the Problem.

Apr 12, 2018

Please, see the proof below

Explanation:

"Reminder"

sin(A+B)=sinAcosB+sinBcosA

cos(A-B)=cosAcosB+sinAsinB

Therefore,

LHS=sin(A+B)/cos(A-B)

=(sinAcosB+sinBcosA)/(cosAcosB+sinAsinB)

=((sinAcosB)/(cosAcosB)+(sinBcosA)/(cosAcosB))/((cosAcosB)/(cosAcosB)+(sinAsinB)/(cosacosB))

=(tanA+tanB)/(1+tanAtanB)

=RHS?

QED