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Math Help - Trig Equality

  1. #1
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    Trig Equality

    When doing some trig practice in my free time, I came across the problem if \sin 2\alpha = \frac{1}{7}, find \sin^4 \alpha + \cos^4 \alpha.

    I did a little research online, and I found that \sin^4 \alpha + \cos^4 \alpha = \frac{1}{4}(\cos 4\alpha + 3), which simplified the problem greatly, and I was able to find that the answer is \frac{97}{98}. Nevertheless, I feel that there is probably a "cleaner" way of doing this that does not require knowing the above equivalence.

    Does anyone have any suggestions on how to attempt this question? Thanks!
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  2. #2
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    Re: Trig Equality

    Use following facts :

    \sin^4 \alpha + \cos^4 \alpha=(\sin^2 \alpha+\cos^2 \alpha)^2-2\sin^2 \alpha \cdot \cos^2 \alpha

    \sin 2 \alpha=2\sin \alpha \cdot \cos \alpha
    Thanks from superbird70
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  3. #3
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    Re: Trig Equality

    Thank you very much! That made it so easy to do!
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