SOLUTION: Prove {{{(tan(A+B)-tan(A))/(1+tan(A+B)tan A)}}}{{{""=""}}}{{{tan(B)}}}

Algebra ->  Trigonometry-basics -> SOLUTION: Prove {{{(tan(A+B)-tan(A))/(1+tan(A+B)tan A)}}}{{{""=""}}}{{{tan(B)}}}      Log On


   

Question 1058324: Prove
%28tan%28A%2BB%29-tan%28A%29%29%2F%281%2Btan%28A%2BB%29tan+A%29%22%22=%22%22tan%28B%29
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

%28tan%28A%2BB%29-tan%28A%29%29%2F%281%2Btan%28A%2BB%29tan+A%29%22%22=%22%22tan%28B%29

We work with the left side

The formula for tan%28alpha-beta%29 is

tan%28alpha-beta%29%22%22=%22%22%28tan%28alpha%29-tan%28beta%29%29%2F%281%2Btan%28alpha%29tan%28beta%29%29

If we substitute alpha=A%2BB and beta=A
in that formula

tan%28%28A%2BB%29-A%29%22%22=%22%22%28tan%28A%2BB%29-tan%28A%29%29%2F%281%2Btan%28A%2BB%29tan%28A%29%29

the right side is the the same as the left side of
the identity we are to prove, so the left side is

tan%28%28A%2BB%29-A%29

which becomes

tan%28A%2BB-A%29

tan%28B%29

Edwin