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Math Help - Trig Identity

  1. #1
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    Trig Identity

    I am failing to realize how do you go from

    cos(2t)+sin(2t)

    to

    \sqrt{2}cos(2t-\frac{\pi}{4})

    I was never good at trig.
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  2. #2
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    \displaystyle \sqrt{2}\cos{\left(2t - \frac{\pi}{4}\right)} = \sqrt{2}\left[\cos{(2t)}\cos{\left(\frac{\pi}{4}\right)} + \sin{(2t)}\sin{\left(\frac{\pi}{4}\right)}\right]

    \displaystyle = \sqrt{2}\left[\frac{\cos{2t}}{\sqrt{2}} + \frac{\sin{2t}}{\sqrt{2}}\right]

    \displaystyle = \cos{2t} + \sin{2t}.
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  3. #3
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    Very much appreciate I am going to have analyze this for a few minutes to understand what identities were used and etc. because that radian number pi/4 really threw me off.
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  4. #4
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    \displaystyle \frac{\pi^C}{4} = 45^{\circ}

    and

    \displaystyle \cos{(A\pm B)} \equiv \cos{A}\cos{B} \mp \sin{A}\sin{B}.
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