Given that cos 2@= 1/9, find cos @ in the form ± √ܽa/ bܾ , where ܽa, ܾb ∈ ℕ is there any way to do this without trigometric formulae @ stands for theta
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$\cos(2 \theta) = \dfrac 1 9$ $2 \cos^2(\theta) - 1 = \dfrac 1 9$ $\cos^2(\theta) = \dfrac {10}{18}$ $\cos(\theta) = \pm \sqrt{\dfrac{10}{18}} = \pm \dfrac{\sqrt{5}}{3}$