Question

If $2 \,\tan ^{2} \theta=\sec ^{2} \theta$, then general value of $\theta$ are

• A. $n \pi \pm \frac{\pi}{4}, n \in I$
• B. $n \pi \pm \frac{\pi}{6}, n \in I$
• C. $2 n \pi+\frac{\pi}{4}, n \in I$
• D. $2 n \pi \pm \frac{\pi}{6}, n \in I$

Answer 1

Answer: (A)

$2 \,\tan ^{2} \theta=\sec ^{2} \theta=1+\tan ^{2} \theta $
$\Rightarrow \tan ^{2} \theta=1=(1)^{2}=\tan ^{2} \frac{\pi}{4}$
$\theta=n \pi \pm \frac{\pi}{4}, n \in I$