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Math Help - Verify identity

  1. #1
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    Verify identity

    am terrible with identity and this book proposes no answers or how to for the HW.

    I can do the examples given okay but when it comes to the homework it's like wtf is all this. The problem is:

    (sin@+cos@)^2=1+sin2@

    i need to verify that one side equals the other.

    only thing i know is that sin2@=2sin@cos@.
    Last edited by Frenchie; August 12th 2010 at 09:01 PM.
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  2. #2
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    The two sides do NOT equal each other.

    \sin^2{\theta} + \cos^2{\theta} \equiv 1 is a well known Identity known as the Pythagorean Identity.


    Since \sin{2\theta} is NOT identically equal to  0, (though it does equal 0 for CERTAIN values of \theta).

    That means that the LHS can not possibly equal the RHS for ALL \theta.
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  3. #3
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    sorry i wrote the problem wrong! I started this a day ago and i typed it from my page not the book.

    It's (sin@+cos@)^2=1+sin2@
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  4. #4
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    (\sin{\theta} + \cos{\theta})^2 = \sin^2{\theta} + 2\sin{\theta}\cos{\theta} + \cos^2{\theta}

     = \sin^2{\theta} + \cos^2{\theta} + 2\sin{\theta}\cos{\theta}

     = 1 + 2\sin{\theta}\cos{\theta}

     = 1 + \sin{2\theta}.
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  5. #5
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    Can i get help with this other one?

    sin2t-tant=tantcost2t

    2sintcost-sint/cost

    (2sintcost^2/cost) - (sint/cost)

    (2sintcost^2 - sint)/cost
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  6. #6
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    \frac{2sintcos^2t - sint}{cost}

    = \frac{sint(2cos^2t - 1)}{cost}

    = tant cos2t
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  7. #7
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    thanks guys, that helped me solving these annoying problems, i'm understanding the more complex ones a little better now. I have an exam on Tuesday >_< gotta keep studying.
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