How would I go on about solving:
$\,\quad\cos\Big(\,2\cdot \arctan\big(\frac{1}{2}\big)\Big)$ ?
My attempt was to find $\,v\,$ in $\,\frac{\sin\left(v\right)}{\cos\left(v\right)} = \frac{1}{2}\,$ and substitute that with $\,\arctan\left(\frac{1}{2}\right),\,$ but I end up with $\,\sin\left(v\right) = \sqrt{\frac{1}{5}}\,$ which I cant solve.
Is there any other way to approach the problem?
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