Results 1 to 2 of 2

Math Help - establish the identity

  1. #1
    Junior Member
    Joined
    Apr 2009
    Posts
    30

    establish the identity

    [(cos(2ɵ)-cos(4ɵ))/(cos(2ɵ)+cos(4ɵ))] - tanɵtan(3ɵ)=0

    thanks guys
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,868
    Thanks
    747
    Hello, Johnny!

    We need two sum-to-product identities:

    . . \cos A - \cos B \;=\;\text{-}2\sin\left(\tfrac{A+B}{2}\right)\sin\left(\tfrac{  A-B}{2}\right)

    . . \cos A + \cos b \:=\:2\cos\left(\tfrac{A+B}{2}\right)\cos\left(\tf  rac{A-B}{2}\right)


    \frac{\cos2\theta-\cos4\theta}{\cos2\theta+\cos4\theta} - \tan\theta\tan3\theta \;=\;0

    The fraction is: . \frac{\text{-}2\sin3\theta\sin(\text{-}\theta)}{2\cos3\theta\cos(\text{-}\theta)} \;=\;\frac{\text{-}\sin3\theta(\text{-}\sin\theta)}{\cos3\theta\cos\theta}\;= . \frac{\sin3\theta\sin\theta}{\cos3\theta\cos\theta  } \;=\;\tan3\theta\tan\theta


    Then the problem becomes: . \tan3\theta\tan\theta - \tan\theta\tan3\theta \;=\;0

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help with De Moivre formula to establish identity
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: December 24th 2011, 11:48 AM
  2. establish the following:
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: March 26th 2010, 12:12 PM
  3. establish the identity
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 1st 2009, 05:50 PM
  4. Establish the trig identity
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: October 9th 2009, 05:19 AM
  5. Establish the Identity
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: August 25th 2008, 09:54 PM

Search Tags


/mathhelpforum @mathhelpforum