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Please help me in these identities

  1. Feb 16, 2009 #1
    Please help me in these identities!!!!

    I tried to solve these identities, but I don't think that these are identities exept the first,
    1.) sin2α/1+cos2α=tanα
    2.) 1-cosα/sinα=tanα/2
    3.) tanα+ctanα=csecα
    4.) 3cosα+cos3α/3sinα-sin3α=3/2
    5.) sin18°+sin30°=sin54

    At first i did this:
    sin2α=2sinα*cosα
    cos2α=cos^2α-sin^2α
    1=cos^2α+sin^2α
    sin2α/1+cos2α=2sinα*cosα/cos^2α+sin^2α+cos^2α-sin^2α=...=tanα

    But I don't know what to do eith others i tried to substitute tanα=sinα/cosα and etc but no solve ,
    please help me
     
  2. jcsd
  3. Feb 16, 2009 #2
    Re: Please help me in these identities!!!!

    please , I need help
     
  4. Feb 16, 2009 #3

    Mark44

    Staff: Mentor

    Re: Please help me in these identities!!!!

    You don't have a single parenthesis in what you show, which probably means that what you think you wrote and what people will read are different.

    For example, in 1, you have sin2α/1+cos2α=tanα.
    Is 1 + cos2a in the denominator? If so, write the equation this way:
    sin2α/(1+cos2α)=tanα

    In 2, do you mean
    (1-cosα)/sinα=(tanα)/2 or
    (1-cosα)/sinα=tan(α/2) or something else?

    In 4, do you mean (3cosα+cos3α)/(3sinα-sin3α)=3/2?

    In the last equation you wrote, you have cos^2a. Do you mean cos^2(a)? You probably do, because cos^(2a) doesn't make any sense.
     
  5. Feb 17, 2009 #4

    Mark44

    Staff: Mentor

    Re: Please help me in these identities!!!!

    Please clarify what you meant for 1, 2, and 4. By that, I mean, if the numerator or denominator (or both) has more than one term, put parentheses around the terms in the numerator and/or denominator.

    Number 5 appears to be true, assuming that what you have on the right side is sin 54°.
     
  6. Feb 19, 2009 #5
    Re: Please help me in these identities!!!!

    Try if these are identities

    sin18°+sin30°=sin54°

    (cos36°)^2 + (sin18°)^2=3/4, please help on these
     
  7. Feb 19, 2009 #6

    Mark44

    Staff: Mentor

    Re: Please help me in these identities!!!!

    I believe that the first one is an identity. The right side is sin(3*18°), and I would start with it.
    sin(3*18°) = sin(2*18° + 18°) = sin(2*18°)cos(18°) + cos(2*18°)sin(18°). Now use the double-angle formulas on that expression and see if that helps. Also, sin(30°) = 1/2.

    For the second, cos(36°) = cos(2*18°). What can you do with that?
     
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