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I am trying to derive the general solution for the equation $ 2 \cos^2 x = 1$

It's get reduced to $ \cos x = \pm \frac1 {\sqrt{2}} $

Now, for, $\cos x = \frac 1 {\sqrt{2}} \Rightarrow x = 2n\pi \pm \frac{\pi}{4}$ and for $\cos x = - \frac 1 {\sqrt{2}} \Rightarrow x = 2n\pi \pm \frac{3\pi}{4}$, but I am stuck here I want to know how to derive the general solution that will satisfy the mother equation ($ 2 \cos^2 x = 1$) itself?

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    You've found all the solutions already, so what's the problem? Anyway, you can also solve the equation by rewriting it as $\cos 2x = 0$.2012-04-08

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Looking at the unit circle, we see that odd integer multiples of $\frac{\pi}{4}$ give all solutions.

If you wish to arrive at this from the equations that you derived, notice that for a given $n$, the solutions corresponding to " $...+\pi /4$ " and " $...-3 \pi /4 $" are pi units apart.

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    Thanks a lot Chaz!! Actually I did the whole thing reverse and also thanks for helping me understand how to get it from my derivation too:)2012-04-08