1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Trigonometry- addition and factor forumla

  1. Nov 23, 2012 #1
    1. The problem statement, all variables and given/known data
    If tan(A+B) = 3 and tan(A-B) = 2, find tan2A and tan2B


    2. Relevant equations
    tan (A - B) = (tan A - tan B)/(1 + (tan A)(tan B) and similar sort of one for tan(A+B)


    3. The attempt at a solution
    i did some calculation and got tanA= (1-2tanB)/5tanB

    after which there seems some thing missing for the proceeding calculations....
    wonder what to do next?
     
  2. jcsd
  3. Nov 23, 2012 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    For better service, try posting your math questions in either the Precalculus math or the Calculus sections of the HW forums.
     
  4. Nov 23, 2012 #3

    Borek

    User Avatar

    Staff: Mentor

    Topic moved. As SteamKing wrote - this is definitely not "OtherSciences", but Math itself.
     
  5. Nov 23, 2012 #4
    The "other identity" of "the sort" you are talking about is given like this:

    [tex]\tan(x+y)=\frac{\sin(x+y)}{\cos(x+y)}=\frac{\sin(x)\cos(y)+\cos(x)\sin(y)}{\cos(x)\cos(y)-\sin(x)\sin(y)}=\frac{\tan(x)+\tan(y)}{1-\tan(x)\tan(y)}[/tex]

    Now, a good start to this question would be to write everything you already have down: (name tan(a)=x and tan(b)=y) [itex]\displaystyle 3=\frac{x+y}{1-xy}[/itex] and [itex]\displaystyle 2=\frac{x-y}{1+xy}[/itex]. Then, these are two equations with two unknowns (a and b.) Try to manipulate the expressions and eliminate a term that you would not want in an equation with two unknowns. The rest follows relatively easily.

    If you found some value for tan A whose inverse tangent is not very pleasant, you are doing something wrong; the value A comes out very nicely.

    Tip: Your expression for tan A is not the simplest one possible. Try to find linear expressions.
    Tip-2: There isn't only one solution.
     
    Last edited: Nov 23, 2012
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Trigonometry- addition and factor forumla
  1. Factor This (Replies: 3)

  2. Factorize (Replies: 6)

  3. Trigonometry Problem (Replies: 3)

Loading...