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

1. ## 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

2. Work it by just knowing that $\cos^2x=1-\sin^2x.$

3. $\begin{gathered}
\sin (x) = 1 + \cos ^2 (x) \hfill \\
\sin (x) = 1 + 1 - \sin ^2 (x) \hfill \\
\sin ^2 (x) + \sin (x) - 2 = 0 \hfill \\
\end{gathered}$

Let $z=\sin(x)$ and solve $z^2 + z -2 =0$.