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

Answer 1

Answer: (A)

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