Question

The value of $\cos [\frac{1}{2}{\cos }^{-1}(\cos (\frac{-14\pi }{5}))]$ is/are:

• A. $\cos (\frac{-7\pi }{5})$
• B. $\sin (\frac{\pi }{10})$
• C. $\cos (\frac{2\pi }{5})$
• D. -$\cos (\frac{3\pi }{5})$

Answer 1

The correct option is A $\cos (\frac{-7\pi }{5})$

$\to cos\left[\frac{1}{2}{cos}^{-1}cos(-14\frac{\pi }{5})\right]$

$\to cos\left[\frac{1}{2}(-14\frac{\pi }{5})\right]=cos[-\frac{7\pi }{5}]$