Question

Solve :
$8{\cos }^3\frac{\pi }{9}-6\cos \frac{\pi }{9}$

Answer 1

$\begin{array}{c}8{\cos }^3\frac{\pi }{9}-6\cos \frac{\pi }{9}\\ =2\cos \frac{\pi }{9}\left[4{\cos }^2\frac{\pi }{9}-3\right]\\ =2\times \cos \frac{\pi }{3}=2\times \frac{1}{2}=1\end{array}$

Hence,

Required answer is 1.