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Math Help - proof of trig identity

  1. #1
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    proof of trig identity

    am trying to prove that \frac {sin4A +sin2A}{cos4A + cos2A} = tan3A
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  2. #2
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    Quote Originally Posted by sigma1 View Post
    am trying to prove that \frac {sin4A +sin2A}{cos4A + cos2A} = tan3A
    Dear sigma1,

    Try using the sum-to-product formula. Hope this will help you!!
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  3. #3
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    i have tried but i seem to be getting no where with this one.
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  4. #4
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    Quote Originally Posted by sigma1 View Post
    i have tried but i seem to be getting no where with this one.
    Dear sigma1,

    You can't be getting no where. Now use, sinA+sinB=2sin\frac{A+B}{2}cos\frac{A-B}{2} for the numerator, and cosA+cosB=2cos\frac{A+B}{2}cos\frac{A-B}{2} for the denominator.

    Hope this will help you.
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  5. #5
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    Hi sigma1,

    if it looks confusing with "A" in both,
    you can rewrite it as

    SinX+SinY=2Sin\left(\frac{X+Y}{2}\right)Cos\left(\  frac{X-Y}{2}\right)

    where X=4A, Y=2A

    and

    CosX+CosY=2Cos\left(\frac{X+Y}{2}\right)Cos\left(\  frac{X-Y}{2}\right)

    When you work this out, you will have cancellation of terms in your fraction,
    leading to the result.
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