Find all solutions to the equation in the interval [0, 2pi). COS X = sin 2x​

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Find all solutions to the equation in the interval [0, 2pi). COS X = sin 2x​

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Thiên Hương 4 years 2021-08-17T17:03:41+00:00 1 Answers 9 views 0

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  1. thanhcong
    0
    2021-08-17T17:05:13+00:00
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    Answer:

    Step-by-step explanation:

    cos x=sin 2x

    sin 2x-cos x=0

    2 sin x cos x-cos x=0

    cos x(2 sin x-1)=0

    either cos x=0

    x=\frac{\pi }{2},\frac{3\pi }{2}

    or

    2 sin x-1=0

    sin x=\frac{1}{2} =sin (\frac{\pi }{6}),sin(\pi -\frac{\pi }{6} )\\x=\frac{\pi }{6} ,\frac{5 \pi }{6}

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