Question

The solution set of $\sec x=\sec (\pi +x)$ is

• A. $x=n\pi ,n\in Z$
• B. $x=2n\pi \pm \frac{\pi }{2},n\in Z$
• C. $x=(2n+1)\frac{\pi }{2},n\in Z$
• D. $x=\varphi$

Answer 1

The correct option is D $x=\varphi$

$\sec x=\sec (\pi +x)\Rightarrow \sec x=-\sec x\Rightarrow 2\sec x=0\Rightarrow \sec x=0$
which is not possible as $|\sec x|\ge 1$