Let $0 < a < \dfrac{\pi}{2}$ and
$$\cos^{2} a - \cos(2a) = \sin(2a)$$
For the value of $a$ satisfying this equality, which of the following is correct?
A) $\tan a = \dfrac{1}{5}$
B) $\cot a = \dfrac{2}{\sqrt{5}}$
C) $\cos a = \dfrac{1}{\sqrt{5}}$
D) $\operatorname{cosec} a = \sqrt{5}$
E) $\sin(2a) = \dfrac{3}{5}$