Question

The general solution(s) of the equation $\cos \theta +\cos 7\theta =0$ can be ($n\in Z$)

• A. $\theta =(2n+1)\frac{\pi }{4}$
• B. $\theta =(2n+1)\frac{\pi }{8}$
• C. $\theta =(2n+1)\frac{\pi }{6}$
• D. $\theta =(2n+1)\frac{\pi }{3}$

Answer 1

Answer: (B), (C)

$\theta =(2n+1)\frac{\pi }{6}$

$\cos \theta +\cos 7\theta =0$
$\Rightarrow 2\cos 4\theta .\cos 3\theta =0$
$\Rightarrow \cos 4\theta =0\text{or}\cos 3\theta =0$
$\Rightarrow 4\theta =(2n+1)\frac{\pi }{2}\text{or}3\theta =(2n+1)\frac{\pi }{2}$
$\Rightarrow \theta =(2n+1)\frac{\pi }{8}\text{or}\theta =(2n+1)\frac{\pi }{6}$