Question

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

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

Answer 1

The correct option is B

$n\mathrm{\pi }\pm \frac{\mathrm{\pi }}{6}$

Explanation for the correct option:

Step 1: Take the square root

Given: $se{c}^2\theta =\frac{4}{3}$

Simplification and calculation of the general value of $\left(\theta \right)$

$\begin{array}{rcl}\therefore sec\left(\theta \right)& =& \sqrt{\frac{4}{3}}\\ & =& \pm \frac{2}{\sqrt{3}}\end{array}$

Step 2 : Put the value of $\mathit{s}\mathit{e}\mathit{c}\left(\frac{\pi }{6}\right)\mathbf{=}\frac{\mathbf{2}}{\sqrt{\mathbf{3}}}$

$\therefore$Value of $\sec \left(\frac{\mathrm{\pi }}{6}\right)=\frac{2}{\sqrt{3}}$

$\Rightarrow \sec \left(\theta \right)=\pm \sec \left(\frac{\mathrm{\pi }}{6}\right)$

General solution of $\left(\theta \right)$ is $n\pi \pm \theta$

$\therefore \left(\theta \right)=n\pi \pm \frac{\mathrm{\pi }}{6}$

Hence, option $\left(\mathrm{B}\right)$ is correct .