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how does $1+\cos2\theta = (2-\sqrt2)/2$ give you $-\sqrt2/2$?

i get that you subtract 1 from the left side, but how does doing so on the right give you $-\sqrt2/2$?

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    An equation like $1+\cos\theta=(2-\sqrt{2})/2$ can only give "true" or "false", but not a number $\ldots$2012-09-02

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$1+\cos 2\theta=\frac{2-\sqrt 2}{2}=\frac{2}{2}-\frac{\sqrt 2}{2}=1-\frac{\sqrt 2}{(\sqrt 2)^2}=1-\frac{1}{\sqrt 2}$

$\implies 1+\cos 2\theta=1-\frac{1}{\sqrt 2}\implies \cos 2\theta=-\frac{1}{\sqrt 2}$