Question

General solution of the equation $\sqrt{3}\sec 3x=2$ is :

• A. $2n\pi \pm \frac{\pi }{18},n\in Z$
• B. $\frac{2n\pi }{3}\pm \frac{\pi }{9},n\in Z$
• C. $n\pi \pm \frac{\pi }{18},n\in Z$
• D. $\frac{2n\pi }{3}\pm \frac{\pi }{18},n\in Z$

Answer 1

The correct option is D $\frac{2n\pi }{3}\pm \frac{\pi }{18},n\in Z$

$\sqrt{3}\sec 3x=2\Rightarrow \cos 3x=\frac{\sqrt{3}}{2}\Rightarrow 3x=2n\pi \pm \frac{\pi }{6}\Rightarrow x=\frac{2n\pi }{3}\pm \frac{\pi }{18},n\in Z$