Question

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

• A. $x=\frac{\pi }{4}$
• B. $x=\frac{\pi }{3}$
• C. $x=\frac{2\pi }{3}$
• D. $x=\frac{3\pi }{4}$

Answer 1

Answer: (A), (B), (D)

The correct options are
A

$x=\frac{\pi }{4}$

B

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

D

$x=\frac{3\pi }{4}$

$cos3x-cos2x+cosx=04co{s}^{3}x-3cosx-2co{s}^{2}x+1+cosx=04co{s}^{3}x-2co{s}^{2}x-2cosx+1=02co{s}^{2}x(2cosx-1)-1(2cosx-1)=0(2co{s}^{2}x-1)(2cosx-1)=0co{s}^{2}x=\frac{1}{2}orcosx=\frac{1}{2}cosx=\frac{1}{2}\Rightarrow x=\frac{\pi }{3}co{s}^{2}x=\frac{1}{2}\Rightarrow cosx=\pm \frac{1}{\sqrt{2}}\Rightarrow x=\frac{\pi }{4}orx=\frac{3\pi }{4}$