Results 1 to 3 of 3

Math Help - Performance Final Done today. Problem on there I could not figure out.

  1. #1
    Member
    Joined
    Dec 2007
    From
    Georgia
    Posts
    85

    Performance Final Done today. Problem on there I could not figure out.

    I got done with it about 2 hours ago, and there was one problem I could not figure out.

    I had to prove that:

    cot x+\frac{sinx}{1+cosx}=cscx

    Could not figure it out to save my life. Could someone show me how to do it?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    \cot (x) + \frac{{\sin (x)}}{{1 + \cos (x)}} = \frac{{\cos (x)}}{{\sin (x)}} + \frac{{\sin (x)}}{{1 + \cos (x)}}
    \frac{{\cos (x)}}{{\sin (x)}} + \frac{{\sin (x)}}{{1 + \cos (x)}} = \frac{{\cos (x) + \cos ^2 (x) + \sin ^2 (x)}}{{\sin (x)\left( {1 + \cos (x)} \right)}} = \frac{1}{{\sin (x)}}<br />
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,678
    Thanks
    610
    Hello, mathgeek777!

    Another approach . . .


    Prove: . \cot x+\frac{\sin x}{1+\cos x}\:=\:\csc x

    Multiply the fraction by . \frac{1-\cos x}{1 - \cos x}

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

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

    . . = \;\;\frac{\cos x}{\sin x} + \frac{1-\cos x}{\sin x} \;\;=\;\;\frac{1}{\sin x} \;\;=\;\;\csc x

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Today's problem that I don't understand.
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: October 6th 2009, 10:39 AM
  2. Final today at 6 - Eigen Values in 3x3 matrix
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 6th 2009, 12:59 PM
  3. Logarithmic Function - Performance Problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 5th 2009, 01:30 AM
  4. Replies: 8
    Last Post: January 20th 2009, 09:49 PM
  5. Need Help, Final TODAY
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 27th 2008, 06:35 AM

Search Tags


/mathhelpforum @mathhelpforum