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Thread: Simple simplify question

  1. #1
    Feb 2009

    Simple simplify question

    Hello fellow mathematicians,

    I've missed few classes and I ran into a big problem while doing a homework.

    My question is going to be very straightforward, and I hopefully will get an answer from you soon.

    Here are the two simple tasks which I'm doing

    My question is, how can I simplify these tasks.

    As for 1341 excercise I want to know a way how to simplify cos 4x and sin 4x.

    And as for 1349 excercise, I would like to know the answer whether there is a way to simplify sin^2x and sin^x.

    I know this may sound funny, but I've forgotten how to do that and was trying all day long to figure out what I'm missing . Thanks for a help in advance.
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  2. #2
    MHF Contributor
    Nov 2008

    You can use the formula

    $\displaystyle \cos 2x = 1-2\sin^2x$

    $\displaystyle \sin 2x = 2\sin x \cos x$

    $\displaystyle \frac{1-cos4x}{sin4x} = \frac{1-(1-2\sin^2 2x)}{2\sin 2x \cos 2x} = \frac{\sin2x}{\cos 2x} = \tan 2x$
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