Results 1 to 5 of 5

Math Help - Proving trig identities

  1. #1
    Junior Member
    Joined
    Jan 2013
    From
    adelaide
    Posts
    26

    Post Proving trig identities

    Hi, I've been working on a question for ages and can't find an answer. This is the first proof I've been asked to do also.

    prove:

    \frac{\sin(x)}{1-\cos(x)} = \csc(x) + \cot(x)

    Am I right in to work the LHS like this:

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

    So,

    \sqrt{1-\cos^2(x)} = 1-\cos(x) ..? For \frac{\sin(x)}{\sin(x)}

    So LHS =1?
    And what do do with the RHS?
    Please help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2011
    From
    Crna Gora
    Posts
    420
    Thanks
    64

    Re: Proving trig identities

    Hint :

    Multiply both numerator and denominator of the LHS fraction by :

    1+\cos x
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2013
    From
    adelaide
    Posts
    26

    Re: Proving trig identities

    Bigger hint?

    So,

    \frac{\sin(\Theta)}{1-cos(\Theta)}\times\frac{1+cos(\Theta)}{1+cos(\Thet  a)}=\frac{sin(\Theta)\times(1+\cos(\Theta)}{1-\cos^2(\Theta)}=\frac{1+\cos(\Theta)}{1-\cos(\Theta)}...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,548
    Thanks
    1418

    Re: Proving trig identities

    Quote Originally Posted by camjerlams View Post
    Bigger hint?

    So,

    \frac{\sin(\Theta)}{1-cos(\Theta)}\times\frac{1+cos(\Theta)}{1+cos(\Thet  a)}=\frac{sin(\Theta)\times(1+\cos(\Theta)}{1-\cos^2(\Theta)}=\frac{1+\cos(\Theta)}{1-\cos(\Theta)}...
    Actually

    \displaystyle \begin{align*} \frac{\sin{(\theta)} \left[ 1 + \cos{(\theta)} \right] }{1 - \cos^2{(\theta)}} &\equiv \frac{\sin{(\theta)} \left[ 1 + \cos{(\theta)} \right] }{ \sin^2{(\theta)} } \\ &\equiv \frac{1 + \cos{(\theta)}}{\sin{(\theta)}} \\ &\equiv \frac{1}{\sin{(\theta)}} + \frac{\cos{(\theta)}}{\sin{(\theta)}} \\ &\equiv \csc{(\theta)} + \cot{(\theta)} \end{align*}
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jan 2013
    From
    adelaide
    Posts
    26

    Re: Proving trig identities

    Ah yeah I totally didn't see the sin^2(x), thanks for that
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proving Trig Identities with Fundamental Identities
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: February 11th 2013, 02:41 AM
  2. Help Proving Trig Identities
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: June 4th 2012, 06:17 PM
  3. Proving Trig Identities
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: March 10th 2010, 05:58 PM
  4. Proving trig identities
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 13th 2009, 05:39 PM
  5. Need proving some trig identities!!!!!
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: July 14th 2007, 06:06 PM

Search Tags


/mathhelpforum @mathhelpforum