Question

Find the general solutions of cos 4x = cos 2x

• A. $x=n\pi$
• B. $x=n\pi \pm \frac{\pi }{6}$
• C. $x=n\pi \pm \frac{\pi }{3}$
• D. $x=n\pi \pm \frac{\pi }{4}$

Answer 1

Answer: (A), (C)

The correct options are
A

$x=n\pi$

C

$x=n\pi \pm \frac{\pi }{3}$

$cos4x=cos2x2co{s}^{2}2x-1-cos2x=0Letcos2x=t2t^2-t-1=0t=\frac{1\pm \sqrt{1-4\times 2\times -1}}{2\times 2}t=\frac{1\pm 3}{4}t=1ort=-\frac{1}{2}cos2x=1orcos2x=-\frac{1}{2}2x=2n\pi or2x=2n\pi \pm \frac{2\pi }{3}x=n\pi orx=n\pi \pm \frac{\pi }{3}$