Results 1 to 3 of 3

Math Help - Identity problem: dont understand Tan3x

  1. #1
    Senior Member
    Joined
    Jul 2006
    From
    Shabu City
    Posts
    381

    Identity problem: dont understand Tan3x

    Prove the identity:
    23.) (tan3x - tanx)/(1 + tan3xtanx) = 2tanx/(1-tan^2 x) <--- tan squared

    elp!!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Aug 2006
    From
    Australia
    Posts
    12
    Quote Originally Posted by ^_^Engineer_Adam^_^
    Prove the identity:
    23.) (tan3x - tanx)/(1 + tan3xtanx) = 2tanx/(1-tan^2 x) <--- tan squared

    elp!!!
     \frac {\tan3x - tanx}{1+\tan3x tanx}

    Use the trig identity:
     tan(A-B) = \frac {tanA - tanB}{1+ tanA tanB}

    = \tan (3x-x)

    = \tan 2x

    Use the trig identity:
    tan2A=  \frac {2tanA}{1 - \tan^2A}

    = \frac{2 tanx}{1- \tan^2x}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,550
    Thanks
    542
    Hello, ^_^Engineer_Adam^_^!


    We also can do it "the long way" . . .

    We're expected to know that: . \tan2x \;=\;\frac{2\tan x}{1 - \tan^2x}\qquad\tan3x \:=\:\frac{\tan2x + \tan x}{1 - \tan2x\tan x}


    Prove the identity: \frac{\tan3x - \tan x}{1 + \tan3x\tan x} \:= \:\frac{2\tan x}{1 -\tan^2\!x}

    The left side is: . \displaystyle{\frac{\left(\frac{\tan 2x + \tan x}{1 - \tan2x\tan x}\right) - \tan x}{1 + \left(\frac{\tan 2x + \tan x}{1 - \tan2x\tan x}\right)\tan x}}


    Multiply top and bottom by 1 - \tan2x\tan x:

    . . \frac{\tan 2x + \tan x - \tan x(1 - \tan 2x\tan x)}{1 - \tan2x\tan x + (\tan2x + \tan x)\tan x}


    We have: . \frac{\tan2x + \tan x - \tan x + \tan2x\tan^2\!x}{1 - \tan2x\tan x + \tan2x\tan x + \tan^2x} = \;\frac{\tan2x + \tan2x\tan^2\!x}{1 + \tan^2x}


    Factor: . \frac{\tan2x(1 + \tan^2\!x)}{1 + \tan^2\!x} \;=\;\tan2x \;= \;\frac{2\tan x}{1 - \tan^2\!x}

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Extra Credit Problem I dont understand at all!
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 9th 2011, 02:49 PM
  2. radical problem, dont understand please help
    Posted in the Algebra Forum
    Replies: 3
    Last Post: July 19th 2011, 02:07 PM
  3. please help i dont really understand this!
    Posted in the Business Math Forum
    Replies: 1
    Last Post: September 7th 2010, 05:24 PM
  4. Replies: 1
    Last Post: October 28th 2009, 10:18 AM
  5. Replies: 2
    Last Post: February 20th 2008, 08:34 PM

Search Tags


/mathhelpforum @mathhelpforum