Question 6
6. Answer the following.
(a) (6 points) Find the exact value of $\sin(2\theta)$, $\cos(2\theta)$, and $\tan(2\theta)$ given
$\cos \theta = -\frac{1}{3}$ in the interval $[\frac{\pi}{2}, \pi]$
(b) (6 points) Prove the following identity
$\frac{2\cos(2x)}{\sin(2x)} = \cot(x) - \tan(x)$