(i)[5]
Show that $2\cos 2x\cos\left(2x+\frac{\pi}{6}\right)$ may be written in the form $k_1(1+\cos 4x)+k_2\sin 4x$, with the constants $k_1$ and $k_2$ to be found.
(ii)[5]
Determine the exact area enclosed by the shaded region.
Mathematics 9709 · AS & A Level · Trigonometry
Trigonometry — practice question
The diagram depicts a section of the curve $y=2\cos 2x\cos\left(2x+\frac{\pi}{6}\right)$. The shaded area is enclosed by the curve and the two coordinate axes.