Results 1 to 4 of 4

Math Help - Proving Trig Identities

  1. #1
    Junior Member casey_k's Avatar
    Joined
    Oct 2008
    From
    Ontario
    Posts
    40

    Post Proving Trig Identities

    I'm having trouble making sense of addition and subtraction in trig identities.

    cos^6x + sin^6x = 1 - 3 sin^2x + 3 sin^4x
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,829
    Thanks
    1602
    Quote Originally Posted by casey_k View Post
    I'm having trouble making sense of addition and subtraction in trig identities.

    cos^6x + sin^6x = 1 - 3 sin^2x + 3 sin^4x
    Notice that \cos^6{x} = (\cos^2{x})^3

     = (1 - \sin^2{x})^3

     = \sum_{k = 0}^{3}\left(_k^n\right)1^{n - k}+(-\sin^2{x})^k

     = 1 - 3\sin^2{x} + 3\sin^4{x} - \sin^6{x}.


    So we can rewrite the original function as

    1 - 3\sin^2{x} + 3\sin^4{x} - \sin^6{x} + \sin^6{x}.

    What does this equal?
    Last edited by Prove It; April 23rd 2009 at 09:40 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,108
    Thanks
    970
    Quote Originally Posted by casey_k View Post
    I'm having trouble making sense of addition and subtraction in trig identities.

    cos^6x + sin^6x = 1 - 3 sin^2x + 3 sin^4x
    two hints ...

    (a^2)^3 + (b^2)^3 = (a^2 + b^2)(a^4 - a^2b^2 + b^4)

    \cos^2{x} = 1 - \sin^2{x}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member casey_k's Avatar
    Joined
    Oct 2008
    From
    Ontario
    Posts
    40
    I didn't get it at first because I expanded the right side both (cos^2x)^3 + (sin^2x)^3 but then I realized I only had to expand cos.

    Thank you!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Proving Trig identities help!
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: March 28th 2011, 05:33 AM
  2. Proving Trig Identities.
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 3rd 2009, 08:57 PM
  3. Proving Trig Identities
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: February 25th 2009, 10:56 AM
  4. Proving Trig Identities?
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: January 7th 2009, 09:24 AM
  5. HELP! Trig-Proving Identities
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 22nd 2006, 09:48 AM

Search Tags


/mathhelpforum @mathhelpforum