# solve the multiple-angle equation. 2cos x/2 - sqrt(2) = 0

solve the multiple-angle equation. $2\mathrm{cos}x/2-\sqrt{\left(}2\right)=0$

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1:
$2\mathrm{cos}\left(x/2\right)-\sqrt{\left(}2\right)=0$
2:
$\mathrm{cos}\left(x/2\right)=\sqrt{\left(}2\right)/2$
3:

4:
$\pi /2=2n\pi$ & $x+7\pi /2+2n\pi$
Result
. It changes from because the equation is $\mathrm{cos}\left(x/2\right)$ and not $\mathrm{cos}x$ so you need to multiply the coterminal possibilities by 2.