# How does this fraction simplify?

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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Well, if you want to subtract two numbers when one or both of them are fractions, it's a good idea to make them both into fractions with the same denominator. You can then just subtract the numerators. So have a think about what the number 1 would look like if you had to write it as a fraction with 2 as the denominator. – user22805 Sep 2 '12 at 5:51
${2-\sqrt2\over2}={2\over2}-{\sqrt2\over2}=1-{\sqrt2\over2}$. – Gerry Myerson Sep 2 '12 at 5:51
So obvious, I can't believe I didn't see that. Gerry thanks a lot. – Kyle H Sep 2 '12 at 5:55
An equation like $1+\cos\theta=(2-\sqrt{2})/2$ can only give "true" or "false", but not a number $\ldots$ – Christian Blatter Sep 2 '12 at 11:40

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