Answer
$\dfrac{119}{169}$
Work Step by Step
$\cos{\theta} = \dfrac{12}{13}$
$\cos{2\theta} =2 \cos^2{\theta} -1 = 2\left(\dfrac{12}{13}\right)^2 -1 $
$\cos{2\theta} = \dfrac{119}{169}$
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