Question

The general solutions for the equation $\cos 4x=\frac{\sqrt{5}+1}{4}$ is

• A. $x=n\pi \pm \frac{\pi }{20},n\in Z$
• B. $x=\frac{n\pi }{2}\pm \frac{\pi }{40},n\in Z$
• C. $x=\frac{n\pi }{4}\pm \frac{\pi }{20},n\in Z$
• D. $x=\frac{n\pi }{2}\pm \frac{\pi }{20},n\in Z$

Answer 1

The correct option is D $x=\frac{n\pi }{2}\pm \frac{\pi }{20},n\in Z$

$\cos 4x=\frac{\sqrt{5}+1}{4}=\cos {36}^{\circ }$
$\Rightarrow \cos 4x=\cos \frac{\pi }{5}$
$\Rightarrow 4x=2n\pi \pm \frac{\pi }{5},n\in Z$
$\Rightarrow x=\frac{n\pi }{2}\pm \frac{\pi }{20},n\in Z$