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Homework Help: Help with proving a trigonometric identity

  1. Feb 26, 2010 #1
    Hi I've got this problem which has really been bothering me.

    How are you supposed to prove that:
    (Sin[A] Sin[2 A] + Sin[3 A] Sin[6 A])/(Sin[A] Cos[2 A] + Sin[3 A] Cos[6 A]) is identicle to tan[5A].

    I am almost sure that I've got to use the factor formulae, but I've had no luck. Maybe someone can help me please :)
    Thank you for your time!
     
  2. jcsd
  3. Feb 26, 2010 #2
    Try to "de-factor".
    For instance, Sin(A)Sin(2A)=Sin(2A)Sin(A).
    Recalling the identity that Cos S + Cos T = ?
     
  4. Feb 26, 2010 #3
    Ok i found out how to work it out. i first multiply by 2 throughout. then i used the factor formulae until i end up with the terms :

    2sin5A sin4A / 2sin4Acos5A which is identicle to sin5A/cos5A which is identicle to tan5A...PROVED!

    The satisfaction of proving an identity or equation is rather incredible!
     
  5. Feb 26, 2010 #4
    yea! Great sense of satisfaction. you are turning 17 this year?
     
  6. Feb 26, 2010 #5
    haha indeed i am, still young i guess, just scratching the surface of mathematics. The subject really gets you thinking
     
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