Can't understand if question is wrong: Given sin(A-B)/sin(A+B)=2/3 , prove tanA=tanB

[lahsim]

Given that sin(A-B)/sin (A+B) = 2/3 , prove that Tan A = Tan B


The problem is that when I work out the first part it gives me sinAcosB=5cosAsinB and that does not equate to sinAcosB=cosAsinB which is derived from Tan A = Tan B

 

[lahsim]

Given that sin(A-B)/sin(A+B) =2/3 , prove that tan A = Tan B


the problem is I derive that sinAcosB=5cosAsinB from the first part and that does not equate to sinAcosB=cosAsinB which is derived from the second part. So I can't prove it ?

 

[Harry_the_cat]

Given that sin(A-B)/sin(A+B) =2/3 , prove that tan A = Tan B


the problem is I derive that sinAcosB=5cosAsinB from the first part and that does not equate to sinAcosB=cosAsinB which is derived from the second part. So I can't prove it ?

Pretty sure there's something wrong with the question.

sin(A-B)/sin(A+B) =2/3 leads to tan A = 5*tan B