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Math Help - Need help solving this equation −sin (2θ) − cos (4θ) = 0

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    Need help solving this equation −sin (2θ) − cos (4θ) = 0

    Can someone help explain to me how to use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). I have tried for some time and have been having quite of bit of difficulty on figuring out how to proceed. Any input will be sincerely appreciated.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Need help solving this equation −sin (2θ) − cos (4θ) = 0

    To make things simpler perhaps, I would suggest letting u=2\theta where 0\le u<4\pi and so the equation becomes:

    -\sin(u)-\cos(2u)=0

    I would suggest using the double-angle identity for cosine \cos(2\theta)=1-2\sin^2(\theta) this was you will obtain a quadratic in \sin(u) which factors nicely.

    Can you proceed?
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