SOLUTION: If tan α = 1/3 and tan β = 1/2 , find tan (α + β).

Algebra ->  Trigonometry-basics -> SOLUTION: If tan α = 1/3 and tan β = 1/2 , find tan (α + β).       Log On


   

Question 1117286: If tan α = 1/3 and tan β = 1/2 , find tan (α + β).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

I'm going to use A in place of alpha, and B in place of beta.

Given Info:
tan%28A%29+=+1%2F3
tan%28B%29+=+1%2F2

Plug the values into the identity below, then simplify
tan%28A%2BB%29+=+%28tan%28A%29%2Btan%28B%29%29%2F%281-tan%28A%29%2Atan%28B%29%29

tan%28A%2BB%29+=+%281%2F3%2B1%2F2%29%2F%281-%281%2F3%29%2A%281%2F2%29%29

tan%28A%2BB%29+=+%282%2F6%2B3%2F6%29%2F%286%2F6-1%2F6%29

tan%28A%2BB%29+=+%285%2F6%29%2F%285%2F6%29

tan%28A%2BB%29+=+%285%2F6%29%2A%286%2F5%29

tan%28A%2BB%29+=+%285%2A6%29%2F%286%2A5%29

tan%28A%2BB%29+=+30%2F30

tan%28A%2BB%29+=+1

Answer: 1