Question

Solve $\cos \theta +\cos 3\theta -2\cos 2\theta =0$

• A. $\theta =(2n+1)\frac{\pi }{4},nϵZ$
• B. $\theta =m\pi ,mϵZ$
• C. $\theta =2m\pi ,mϵZ$
• D. $\theta =(2n+1)\frac{\pi }{8},nϵZ$

Answer 1

Answer: (A), (C)

$\theta =(2n+1)\frac{\pi }{4},nϵZ$
$\theta =2m\pi ,mϵZ$

We have $\cos \theta +\cos 3\theta -2\cos 2\theta =0$

$2\cos 2\theta \cos \theta -2\cos 2\theta =0$

$2\cos 2\theta (\cos \theta -1)=0$

$\cos 2\theta =0$ or $\cos \theta -1=0$

$\Rightarrow$ $2\theta =(2n+1)\frac{\pi }{2},n\in Z$ or $\theta =2m\pi ,m\in Z$

$\theta =(2n+1)\frac{\pi }{4},n\in Z$ or $\theta =2m\pi ,m\in Z$