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

Question

11127 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-12T16:30:53

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

Check the Problem.

Answer 2 · 2018-04-12T16:30:55

Please, see the proof below

#"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#