Question

If ${\sec }^2\theta =\frac{4}{3}$, then the general value of $\theta$ is

• A. $2n\pi \pm \frac{\pi }{6}$
• B. $n\pi \pm \frac{\pi }{6}$
• C. $2n\pi \pm \frac{\pi }{3}$
• D. $n\pi \pm \frac{\pi }{3}$

Answer 1

Answer: (B)

We have ${\sec }^2\theta =\frac{4}{3}$
$\Rightarrow {\cos }^2\theta =\frac{3}{4}$
$\Rightarrow {\cos }^2\theta ={\cos }^2\left(\frac{\pi }{6}\right)$
$\Rightarrow \theta =n\pi \pm \frac{\pi }{6}\dots \dots \dots$