Results 1 to 5 of 5

Math Help - arctan(1/3)+arctan(1/2)

  1. #1
    Junior Member
    Joined
    Jan 2008
    Posts
    45

    arctan(1/3)+arctan(1/2)

    simplify: Tan-1(1/3)+tan-1(1/2)

    is there an algebraeic way to do this?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by JOhkonut View Post
    simplify: Tan-1(1/3)+tan-1(1/2)

    is there an algebraeic way to do this?
    Yes.

    Oh, now you want to see a way ......

    There are many ways. Here's a simple but brutal one (watch out for falling Grand Pianos):


    Let \tan \alpha = \frac{1}{3} and \tan \beta = \frac{1}{3}.


    Then \tan (\alpha + \beta) = \frac{\tan \alpha + \tan \beta}{1 - \tan \alpha \tan \beta} = \frac{\frac{1}{3} + \frac{1}{2}}{1 - \left( \frac{1}{3} \right) \left( \frac{1}{2} \right)} = 1.


    Therefore \alpha + \beta = \tan^{-1} \left( \frac{1}{3}\right) + \tan^{-1} \left( \frac{1}{2}\right) = \tan^{-1} (1)  = \frac{\pi}{4}.

    Bet you didn't see that coming
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member topher0805's Avatar
    Joined
    Jan 2008
    From
    Vancouver
    Posts
    336
    I think the easiest way is to just use the special triangles. Does that not work in this case?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by topher0805 View Post
    I think the easiest way is to just use the special triangles. Does that not work in this case?
    Well it's your suggestion, sport. So why don't you try it - see if it does work ....
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member topher0805's Avatar
    Joined
    Jan 2008
    From
    Vancouver
    Posts
    336
    Oh, I see. 2 is never an adjacent side. Disregard my last post.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. arctan(y) = x^2 + C, y = ?
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: October 17th 2010, 03:39 AM
  2. Need help with arctan
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: February 8th 2010, 09:10 PM
  3. arctan
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: March 27th 2009, 11:46 AM
  4. arctan(x)
    Posted in the LaTeX Help Forum
    Replies: 6
    Last Post: June 2nd 2008, 08:51 PM
  5. Cot/Arctan
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: March 27th 2008, 09:13 PM

Search Tags


/mathhelpforum @mathhelpforum