Question

$\{x\in R:\cos 2x+2{\cos }^{2}x=2\}$ is equal to

• A. $\{2n\pi +\frac{\pi }{3}:n\in Z\}$
• B. $\{n\pi \pm \frac{\pi }{6}:n\in Z\}$
• C. $\{n\pi +\frac{\pi }{3}:n\in Z\}$
• D. $\{2n\pi -\frac{\pi }{3}:n\in Z\}$

Answer 1

The correct option is B $\{n\pi \pm \frac{\pi }{6}:n\in Z\}$

Given equation is $\cos 2x+2{\cos }^{2}x=2$
$\Rightarrow 2{\cos }^{2}x–1+2{\cos }^{2}x=2$
$\Rightarrow 4{\cos }^{2}x=3$
$\Rightarrow {\cos }^{2}x=\frac{3}{4}$
$\Rightarrow {\cos }^{2}x={\cos }^2\frac{\pi }{6}$
$\Rightarrow x=n\pi \pm \frac{\pi }{6}:n\in Z$