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Trigonometric Identities - Help!!

Discussion in 'Mathematics' started by Bev179, Mar 28, 2011.

  1. I wonder if anybody could help explain please.

    How to verify the trigonometric identity of this equation or if you could point me in the right direction of a good website

    (cos? - cos³?) / (?(1-cos^2 ?)) = cos ec?


    Thanks

    Bev
     
  2. Is that (cos theta minus cos cubed theta) over the square root of (1 minus cos squared theta)? And should it equal cosec theta?
     
  3. arsinh

    arsinh New commenter

    The two sides are not identical.
     
  4. So is it an equation to solve, rather than an identity to prove?
     
  5. Sorry. Son copied in two different questions :( Perhaps that is adding to his problems



    Again

    cos theta - cos cubed theta

    over

    Sin theta

    equals

    sin theta cos theta
     
  6. arsinh

    arsinh New commenter

    Factorise the numerator.
    Use sin²x = 1 - cos²x twice.


     
  7. In that case, factorise the numerator to give cos theta (1 minus cos squared theta) over sin theta. 1 minus cos squared theta is sin squared theta, so you have cos theta sin squared theta over sin theta and cancel one of the sin thetas.
    Sorry that my lack of ICT skills means that I have to type out the words, but I hope this helps.
    I have a whole book of these called "Trig or treat" but I don't think the author's idea of a treat matches that of the average sixth former!
     
  8. Cross posted with arsinh who was significantly more succinct than me!
     
  9. Thanks Shazgo and Arsinh, you've both been a big help.


    :) I think he's got it.
     

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