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Math Help - Simplifying an equation using trig identities

  1. #1
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    Simplifying an equation using trig identities

    Hi,

    I need to simplify this equation:

    \sqrt{(-2\sin{2t})^2 + (2\cos{2t})^2}

    I know that this equals 2 (by plugging into a calculator). However, I can't figure out the steps to simplify it. This is what I have... could someone show me what I'm doing wrong?

    \sqrt{-4\sin^2{2t} + 4\cos^2{2t}}

    \sqrt{4(\cos^2{2t} - \sin^2{2t})}

    2 \sqrt{1 - 2\sin^2{2t}}

    but I'm not sure where to go from here...
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  2. #2
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    (-2\sin{2t})^2 = 4\sin^2{2t}.

    So you should actually have

    \sqrt{(-2\sin{2t})^2 + (2\cos{2t})^2} = \sqrt{4\sin^2{2t} + 4\cos{2t}}

     = \sqrt{4(\sin^2{2t} + \cos^2{2t})}.

    Go from here.
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  3. #3
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    Oh... then I just use cos^2 + sin^2 = 1, and it's easy.

    Thanks so much for showing me my mistake!
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