Find the principal solutions of cos 3x - cos 2x + cos x = 0

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Question

Find the principal solutions of cos 3x - cos 2x + cos x = 0

Options:

A .

x = \frac{π}{4}

B .

x = \frac{π}{3}

C .

x = \frac{2 π}{3}

D .

x = \frac{3 π}{4}

Answer: Option A
:
A, B, and D

$c o s 3 x - c o s 2 x + c o s x = 0 4 c o s^{3} x - 3 c o s x - 2 c o s^{2} x + 1 + c o s x = 0 4 c o s^{3} x - 2 c o s^{2} x - 2 c o s x + 1 = 0 2 c o s^{2} x (2 c o s x - 1) - 1 (2 c o s x - 1) = 0 (2 c o s^{2} x - 1) (2 c o s x - 1) = 0 c o s^{2} x = \frac{1}{2} o r c o s x = \frac{1}{2} c o s x = \frac{1}{2} \Rightarrow x = \frac{π}{3} c o s^{2} x = \frac{1}{2} \Rightarrow c o s x = \pm \frac{1}{\sqrt{2}} \Rightarrow x = \frac{π}{4} o r x = \frac{3 π}{4}$

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