Results 1 to 6 of 6

Math Help - Trig identities

  1. #1
    Member
    Joined
    Dec 2007
    Posts
    90

    Trig identities

    1 / cos^4ф - 1 / cos^2ф = tan^4ф + tan^2ф
    Last edited by gracey; February 20th 2008 at 03:39 AM.
    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 gracey View Post
    cos^4 ф - sin^4 ф + 1 = 2cos^2ф

    Mr F says: Note that \cos^4 \phi - \sin^4 \phi = (\cos^2 \phi + \sin^2 \phi)(\cos^2 \phi - \sin^2 \phi) = \cos^2 \phi - \sin^2 \phi
    [snip]
    ..
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by gracey View Post
    [snip]
    1 / cos^4ф - 1 / cos^2ф = tan^4ф + tan^2ф
    Right Hand Side \, =\tan^4 \phi + \tan^2 \phi = \frac{\sin^4 \phi}{\cos^4 \phi} + \frac{\sin^2 \phi}{\cos^2 \phi}.

    Now note that:

    \frac{\sin^4 \phi}{\cos^4 \phi} = \frac{(\sin^2 \phi)^2}{\cos^4 \phi} = \frac{(1 - \cos^2 \phi)^2}{\cos^4 \phi} = \frac{1 - 2 \cos^2 \phi + \cos^4 \phi}{\cos^4 \phi} = \frac{1}{\cos^4 \phi} - \frac{2}{\cos^2 \phi} + 1.


    \frac{\sin^2 \phi}{\cos^2 \phi} = \frac{1 - \cos^2 \phi}{\cos^2 \phi} = \frac{1}{\cos^2 \phi} - 1.


    Therefore the right hand side becomes .......
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Mar 2008
    Posts
    14
    I did this one differently. I went like...

    left side
    step one multiply \frac{1}{cos^2x} by \frac{cos^2x}{cos^2x} and then add because we've achieved a common denominator.
    Then using the pythagorean identity, we can change 1-cos^2x into sin^2x

    Right side
    convert the tan's into their proper sin and cosine values.
    multiply {sin^2x}{cos^2x} by \frac{cos^2x}{cos^2x} and add because we've achieved a common denominator.
    factor out a sin^2x
    use the pythagorean identity to turn sin^2x+cos^2x into 1
    finally we end up with \frac{sin^2x}{cos^4x}

    L=R
    Attached Thumbnails Attached Thumbnails Trig identities-.jpg   Trig identities-bb.jpg  
    Last edited by mrbuttersworth; April 22nd 2008 at 01:09 PM. Reason: Changed messy writing into LaTex. Just found out how to use it, thought I'd get some practise.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Mar 2008
    Posts
    14
    Also, I would like to know how to write equations neater and more aesthetically pleasing than the method i'm using now. How do you guys do it?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by mrbuttersworth View Post
    Also, I would like to know how to write equations neater and more aesthetically pleasing than the method i'm using now. How do you guys do it?
    Read this.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trig Identities
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 3rd 2009, 07:44 AM
  2. Trig identities
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: June 22nd 2009, 07:58 AM
  3. Trig Identities
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: November 9th 2008, 05:35 PM
  4. Trig Identities
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: November 7th 2008, 09:25 PM
  5. Trig Identities Help!!!!
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: April 14th 2008, 12:47 PM

Search Tags


/mathhelpforum @mathhelpforum