Q. The greatest value of $\cos\theta$ for which $\cos{5\theta = 0}$, is
A) 0
B) $\frac{1 + \sqrt{5}}{4}$
C) $\sqrt{\frac{5 + \sqrt{5}}{8}}$
D) $\sqrt{\frac{\sqrt{5} + 1}{4}}$
Explanation
(c)
Given, $\cos{5\theta = 0}$
$\Rightarrow 5\theta = \frac{\pi}{2} \Rightarrow \theta = \frac{\pi}{10}$
$\therefore\cos{\theta = \cos{\left( \frac{\pi}{10} \right) = \sqrt{\frac{10 + 2\sqrt{5}}{16}}}}$
$= \sqrt{\frac{5 + \sqrt{5}}{8}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.