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

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

    I'm having trouble finding x for the folowing identity
    sin(x) = 1 + cos^2(x)

    I can see that x is 2k*PI + PI/2 but how do you proove it( I tried doing it but got weird results) and are there other values that satisfy the equation?

    pls help
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  2. #2
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    Work it by just knowing that $\displaystyle \cos^2x=1-\sin^2x.$
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  3. #3
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    $\displaystyle \begin{gathered}
    \sin (x) = 1 + \cos ^2 (x) \hfill \\
    \sin (x) = 1 + 1 - \sin ^2 (x) \hfill \\
    \sin ^2 (x) + \sin (x) - 2 = 0 \hfill \\
    \end{gathered} $
    Let $\displaystyle z=\sin(x)$ and solve $\displaystyle z^2 + z -2 =0$.
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