1. Sketch the curve

   $$y=\sec (2x),0\le x\le 2\pi$$

2. Solve the equation

   $$2\cos (x)\sec (2x)=-1,-2\pi \le x\le 2\pi$$

To sketch $y=\sec (2x)$, first sketch $\cos (x)$, use that to sketch $\sec (x)$, then apply a scale factor enlargement in the $x$ direction.

To solve the equation, rewrite it as

and apply a double angle formula to $\cos (2x)$.