Results 1 to 9 of 9

Math Help - Verify the Trig Identity

  1. #1
    Newbie
    Joined
    Dec 2008
    Posts
    4

    Red face Verify the Trig Identity

    I've been working on this for a few hours... I have a mental block...

    Verify the Identity:

    [sin(2x)+sin(4x)] / [cos(2x) + cos(4x)] = tan(3x)


    thanks so much, in advance
    Follow Math Help Forum on Facebook and Google+

  2. #2
    TD!
    TD! is offline
    Senior Member
    Joined
    Jan 2006
    From
    Brussels, Belgium
    Posts
    405
    Thanks
    3
    This should be easy if you can use Simpson's formulas (equations (1) and (3)) in the numerator and denominator...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2008
    Posts
    4
    ..working it...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Dec 2008
    Posts
    4
    Very easy with Simpson's !!!!
    Unfortunately, I'm in 11th grade Math and all we have to work with are sum/Difference/double angle identities... any more suggestions ???
    Follow Math Help Forum on Facebook and Google+

  5. #5
    TD!
    TD! is offline
    Senior Member
    Joined
    Jan 2006
    From
    Brussels, Belgium
    Posts
    405
    Thanks
    3
    It's indeed very easy with Simpson's.

    If you can only use the multiple-angle formulas, I'm afraid it will be a bit more tricky. I don't see an elegant way just at first sight - you could reduce it all to angle x...
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Dec 2008
    Posts
    4

    Solved !!

    Looks like the function sum/diff (alias Simpson's .... is he taking credit for this these days ) was in my notes...

    So I can use "Simpson's" ...
    Thanks so much !!!!
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,678
    Thanks
    609
    (Happy)Hello, poolshark!

    It's easy if we are allowed the Sum-to-Product identities:

    . . \begin{array}{ccc}\sin A + \sin B &=& 2\sin\left(\frac{A+B}{2}\right)\cos\left(\frac{A-B}{2}\right) \\ \\ [-3mm]<br /> <br />
\cos A + \cos B &=& 2\cos\left(\frac{A+B}{2}\right)\cos\left(\frac{A-B}{2}\right) \end{array}



    Verify the identity: . \frac{\sin2x+ \sin4x} {\cos2x + \cos4x} \:=\: \tan3x\
    The numerator is: . \sin4x + \sin 2x \:=\:2\sin3x\cos x

    The denominator is: . \cos4x+\cos2x \:=\:2\cos3x \cos x


    The fraction becomes: . \frac{{\color{blue}\rlap{/}}2\sin3x{\color{red}\rlap{/////}}\cos x}{{\color{blue}\rlap{/}}2\cos3x{\color{red}\rlap{/////}}\cos x} \;=\;\frac{\sin3x}{\cos3x} \;=\;\tan3x

    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member Khaali91's Avatar
    Joined
    Oct 2008
    From
    Miami
    Posts
    35
    wow the teacher never taught us this in precal..
    Last edited by mr fantastic; December 22nd 2008 at 03:30 AM.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    TD!
    TD! is offline
    Senior Member
    Joined
    Jan 2006
    From
    Brussels, Belgium
    Posts
    405
    Thanks
    3
    Quote Originally Posted by poolshark View Post
    Looks like the function sum/diff (alias Simpson's .... is he taking credit for this these days ) was in my notes...

    So I can use "Simpson's" ...
    Thanks so much !!!!
    I thought this would be the case, the problem "screams" for Simpson's
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Verify the following identity...Need help
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: January 25th 2010, 10:26 PM
  2. verify an identity
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: September 1st 2009, 07:02 AM
  3. Verify Identity
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: May 4th 2009, 01:52 PM
  4. Yet another "Verify the trig identity" prob...HELP
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: December 8th 2008, 06:36 AM
  5. Verify trig identity
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 25th 2007, 01:12 PM

Search Tags


/mathhelpforum @mathhelpforum