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Thread: Trigonometry

  1. #1
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    Trigonometry

    Why does $\displaystyle \cos x \cos (\pi / 4) -\sin x \sin (\pi/4)$ equal $\displaystyle \frac{1}{\sqrt2}(\cos x - \sin x)$?

    Thanks in advance.
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by Air View Post
    Why does $\displaystyle \cos x \cos (\pi / 4) -\sin x \sin (\pi/4)$ equal $\displaystyle \frac{1}{\sqrt2}(\cos x - \sin x)$?

    Thanks in advance.
    $\displaystyle \cos (\pi / 4) = \sin (\pi / 4) = \frac{1}{\sqrt{2}}$
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  3. #3
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    what is $\displaystyle \cos \frac{\pi}{4}$ ? and $\displaystyle \sin \frac{\pi}{4}$

    Did you notice that this can also be written as $\displaystyle \cos (x +\frac{\pi}{4})$ ?

    Bobak
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