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

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Question

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

Options:

A .

x = n π

B .

x = n π \pm \frac{π}{6}

C .

x = n π \pm \frac{π}{3}

D .

x = n π \pm \frac{π}{4}

Answer: Option A
:
A and C

$c o s 4 x = c o s 2 x 2 c o s^{2} 2 x - 1 - c o s 2 x = 0 L e t c o s 2 x = t 2 t^{2} - t - 1 = 0 t = \frac{1 \pm \sqrt{1 - 4 \times 2 \times - 1}}{2 \times 2} t = \frac{1 \pm 3}{4} t = 1 o r t = - \frac{1}{2} c o s 2 x = 1 o r c o s 2 x = - \frac{1}{2} 2 x = 2 n π o r 2 x = 2 n π \pm \frac{2 π}{3} x = n π o r x = n π \pm \frac{π}{3}$

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