Answer
$1$
Work Step by Step
The trigonometric ratios are as follows: $\sin \theta= \dfrac{opposite}{hypotenuse}$ ; $\cos \theta= \dfrac{Adjacent}{hypotenuse}$ and $\tan \theta= \dfrac{Opposite}{Adjacent}$
Now, $\sec \theta= \dfrac{1}{\dfrac{Adjacent}{hypotenuse}}$
So, $\cos (\dfrac{2 \pi}{9}) \times \sec (\dfrac{2 \pi}{9})=\cos (\dfrac{2 \pi}{9}) \times \dfrac{1}{\cos (\dfrac{2 \pi}{9})}$
Our required answer is: $1$
