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Math Help - Trigonometric Equation

  1. #1
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    Aug 2007
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    Trigonometric Equation

    Question please everyone, I'm a bit stumped on this problem. For it I have to find the general solutions.

    The problem is:

    2cos^2(x) = 1 + sin(x)

    I'm just stumped as to how to solve the problem, do I use a power reducing formula or?

    Thanks everyone!
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  2. #2
    Member
    Joined
    Aug 2007
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    144
    Hi WolfMV,

    Note that \sin^2 x+\cos^2 x=1 and so \cos^2 x=1-\sin^2 x thus the equation 2\cos^2 x=1+\sin x becomes 2-2\sin^2 x=1+\sin x . Rearranging gives 2\sin^2 x+\sin x-1=0 and we can see that (2\sin x-1)(\sin x +1)=0 .

    Hope this helps.
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  3. #3
    Member
    Joined
    Dec 2008
    From
    Auckland, New Zealand
    Posts
    189
    Hint:
    Use the trig identity \cos{(2x)} = 1 - 2\sin^2{(x)}
    A quadratic equation will be formed which you can solve to find x.
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