Question

If $x=\sec \theta +\tan \theta$, then $x+\frac{1}{x}=$

• A. $1$
• B. $2\sec \theta$
• C. $2$
• D. $2\tan \theta$

Answer 1

Answer: (B)

Given that, $x=\sec \theta +\tan \theta$
$\Rightarrow x+\frac{1}{x}=\sec \theta +\tan \theta +\frac{1}{\sec \theta +\tan \theta }$
$=\sec \theta +\tan \theta +\sec \theta -\tan \theta =2\sec \theta$