Results 1 to 2 of 2

Math Help - Trig Identities

  1. #1
    Newbie
    Joined
    Oct 2006
    Posts
    18

    Trig Identities

    I am trying to solve the next trig identity however I can't figure it out after I convert the "1"s into cos^2 + sin^2.
    \frac {1+cos x} {sin x} + \frac {sin x} {1+cos x} = \frac {2} {sin x}
    I was also wondering if there's any way to convert the two into 2(cos^2 + sin^2)?
    Thanks,
    Last edited by Universe; January 22nd 2008 at 05:36 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,915
    Thanks
    779
    Hello, Universe!

    \frac {1+\cos x} {\sin x} + \frac {\sin x} {1+\cos x} \:= \:\frac {2}{\sin x}
    Just add the two fractions . . .


    \frac{1+\cos x}{\sin x}\cdot{\color{blue}\frac{1+\cos x}{1+\cos x}} + \frac{\sin x}{1 + \cos x}\cdot{\color{blue}\frac{\sin x}{\sin x}} \;\;=\;\;\frac{(1+\cos x)^2}{\sin x(1+\cos x)} + \frac{\sin^2x}{\sin x(1+\cos x)}

    . . = \;\;\frac{1 + 2\cos x + \overbrace{\cos^2\!x + \sin^2x}^{\text{This is 1}}}{\sin(1+\cos x)} \;\;=\;\;\frac{2 + 2\cos x}{\sin x(1 + \cos x)}

    . . = \;\;\frac{2(1+\cos x)}{\sin x(1+\cos x)} \;\;=\;\;\frac{2}{\sin x}


    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