Question

If $\cos \theta =\frac{1}{2}(x+\frac{1}{x})$, then what is the value of $\cos 2\theta$?

Answer 1

$\cos 20=2{\cos }^2\theta -1$
$=2\left[\frac{1}{4}{(x+\frac{1}{x})}^2\right]-1$
$=\frac{1}{2}(x^2+\frac{1}{x^2}+2)-1$
$=\frac{1}{2}(x^2+\frac{1}{x^2})$