Results 1 to 3 of 3

Math Help - Struggling to prove Trig Identity

  1. #1
    Junior Member
    Joined
    Mar 2014
    From
    Canada
    Posts
    42

    Struggling to prove Trig Identity

    Hi,

    I am struggling with trying to prove:

    [sin^2(x) +4sin(x) + 3] / cos^2(x) = [3+sin(x) / 1 - sin(x)]

    If someone could please walk me through this as well as explaining some tips as to how i can approach similar problems in the future it would be greatly appreciated.
    Have tried applying all the identities but I am obviously missing something which is probably obvious...

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Feb 2014
    From
    United States
    Posts
    662
    Thanks
    340

    Re: Struggling to prove Trig Identity

    Quote Originally Posted by andy000 View Post
    Hi,

    I am struggling with trying to prove:

    [sin^2(x) +4sin(x) + 3] / cos^2(x) = [3+sin(x) / 1 - sin(x)]

    If someone could please walk me through this as well as explaining some tips as to how i can approach similar problems in the future it would be greatly appreciated.
    Have tried applying all the identities but I am obviously missing something which is probably obvious...

    Thanks
    I am not sure I can give a general tip on proofs other than trying different ideas out. What do I mean by that?

    Let's take this case. I see that what is to be proved is in terms of sine functions and what is given is in terms of sines and cosines, more specifically a cosine squared function. Do I know anything about the relationship about the squares of sines and cosines? I certainly do. So I also can "see" that I can eliminate the squared cosine and get everything in terms of sines and squares of sines. Does that help me? I don't know, but it certainly gives me something to try so

    $\dfrac{sin^2(x) + 4sin(x) + 3}{cos^2(x)} = \dfrac{sin^2(x) + 4sin(x) + 3}{1 - sin^2(x)}.$

    Here is a trick that is sometimes useful. I have a function that is a built up from a single function, in this case the sine function. It sometimes helps "seeing" how to proceed by simplifying using a substitution.

    $Let\ u = sin(x).\ Then\ \dfrac{sin^2(x) + 4sin(x) + 3}{1 - sin^2(x)} = what.$

    Can you simplify further now?
    Last edited by JeffM; March 15th 2014 at 07:32 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2014
    From
    Canada
    Posts
    42

    Re: Struggling to prove Trig Identity

    Hi Jeff,

    I have solved it now by finding the factors and cancelling. Thank you so much for your help, really appreciate you taking the time.

    Andy
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove a trig identity
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: May 26th 2012, 01:56 AM
  2. Trying to prove a trig identity
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: May 31st 2009, 04:00 PM
  3. Prove the following Trig Identity
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: April 2nd 2009, 07:56 AM
  4. Prove this trig identity.
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: November 26th 2008, 09:38 AM
  5. Prove Trig Identity
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: November 8th 2008, 01:01 PM

Search Tags


/mathhelpforum @mathhelpforum