Q31 / 100 · BITSAT 2023 (Memory Based Paper 1) · Mathematics
If $\sec ^2 \theta=\frac{4}{3}$, then the general value of $\theta$ is
- A$2 \mathrm{n} \pi \pm \frac{\pi}{6}$
- Correct answerB$\mathrm{n} \pi \pm \frac{\pi}{6}$
- C$2 \mathrm{n} \pi \pm \frac{\pi}{3}$
- D$\mathrm{n} \pi \pm \frac{\pi}{3}$
Solution
We have $\sec ^2 \theta=\frac{4}{3} \Rightarrow \cos ^2 \theta=\frac{3}{4}$
$\Rightarrow \cos ^2 \theta=\cos ^2\left(\frac{\pi}{6}\right) \Rightarrow$
$\theta=n \pi \pm \frac{\pi}{6} \ldots \ldots \ldots$
$\Rightarrow \cos ^2 \theta=\cos ^2\left(\frac{\pi}{6}\right) \Rightarrow$
$\theta=n \pi \pm \frac{\pi}{6} \ldots \ldots \ldots$
Hence, the correct answer is option: 'B'.