Question

If ${\cos }^{2}2x+2{\cos }^{2}x=1,x\in (-\pi ,\pi )$, then $x$ can take the values

• A. $\pm \frac{\pi }{2}$
• B. $\pm \frac{\pi }{4}$
• C. $\pm \frac{3\pi }{4}$
• D. None of these

Answer 1

Answer: (B), (C)

$\pm \frac{\pi }{4}$
$\pm \frac{3\pi }{4}$

Given, ${\cos }^{2}2x+2{\cos }^{2}x=1\Rightarrow 2{\cos }^{2}x-1+{\cos }^{2}x=1\Rightarrow 4{\cos }^{2}x=2\Rightarrow {\cos }^{2}x=\frac{1}{2}\Rightarrow \cos x=\pm \frac{1}{\sqrt{2}}$