Results 1 to 6 of 6

Math Help - Can someone help me prove these two identities?

  1. #1
    Newbie
    Joined
    Apr 2010
    Posts
    6

    Can someone help me prove these two identities?

    Can someone help me prove these two identities?

    I have to prove these two identities and they're really giving me a hard time :/
    I need to see all the steps taken.


    1) sin^4 β - cos^4 β = 1 - 2cos^2 β

    2) cos Φ/(1 + sinΦ) + (1 + sin Φ)/cos Φ = 2sec Φ


    thank youuuu!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by dlngoal View Post
    Can someone help me prove these two identities?

    I have to prove these two identities and they're really giving me a hard time :/
    I need to see all the steps taken.


    1) sin^4 β - cos^4 β = 1 - 2cos^2 β

    2) cos Φ/(1 + sinΦ) + (1 + sin Φ)/cos Φ = 2sec Φ


    thank youuuu!
    For number 1 use the difference of two squares

    (\sin^2 \beta - \cos^2 \beta)(\sin^2 \beta + \cos^2 \beta)

    Use the Pythagorean identity to solve
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,547
    Thanks
    539
    Hello, dlngoal!

    2)\;\;\frac{\cos\phi}{1 + \sin\phi} + \frac{1 + \sin\phi}{\cos\phi} \:=\: 2\sec\phi

    On the left side, multiply the first fraction by \frac{1-\sin\phi}{1-\sin\phi}

    . . \frac{\cos\phi}{1+\sin\phi}\cdot{\color{blue}\frac  {1-\sin\phi}{1-\sin\phi}} + \frac{1+\sin\phi}{\cos\phi} \;\;=\;\;\frac{\cos\phi(1-\sin\phi)}{1-\sin^2\!\phi} + \frac{1+\sin\phi}{\cos\phi}

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

    . . . . . =\;\;\frac{1-\sin\phi + 1 + \sin\phi}{\cos\phi} \;\;=\;\;\frac{2}{\cos\phi} \;\;=\;\;2\sec\phi

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Apr 2010
    Posts
    6
    Thank you Soroban!

    And e^(i*pi), I was told I had to use trigonometric identity formulas and i have to prove that, for number one,

    sin^4 β - cos^4 β = 1 - 2cos^2 β

    that the Left side and the right side are truly equal to each other. I still don't understand. :|
    Follow Math Help Forum on Facebook and Google+

  5. #5
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by dlngoal View Post
    Thank you Soroban!

    And e^(i*pi), I was told I had to use trigonometric identity formulas and i have to prove that, for number one,

    sin^4 β - cos^4 β = 1 - 2cos^2 β

    that the Left side and the right side are truly equal to each other. I still don't understand. :|
    The identity to use is \sin^2 A + \cos^2 A = 1

    Using the difference of two squares:

    (\sin ^2 \beta - \cos^2 \beta)(\sin^2 \beta + \cos ^2 \beta) = \sin ^2 \beta - \cos ^2 \beta = (1-\cos^2 \beta) - \cos^2 \beta = 1-2\cos^2 \beta
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10
    Quote Originally Posted by dlngoal View Post
    Thank you Soroban!

    And e^(i*pi), I was told I had to use trigonometric identity formulas and i have to prove that, for number one,

    sin^4 β - cos^4 β = 1 - 2cos^2 β

    that the Left side and the right side are truly equal to each other. I still don't understand. :|
    Hi dlngoal:

    I did this for you a few days ago. here's the link:

    http://www.mathhelpforum.com/math-he...-identity.html
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Can't prove these identities?
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: November 20th 2010, 07:07 AM
  2. Prove Identities
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 26th 2010, 10:42 PM
  3. Prove these identities.
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: July 20th 2009, 09:42 PM
  4. prove identities
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: June 25th 2009, 11:08 PM
  5. Prove the following identities.............
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: July 16th 2008, 08:07 AM

Search Tags


/mathhelpforum @mathhelpforum