Question

If $\sec \theta =m$ and $\tan \theta =n$, then $\frac{1}{m}\left[(m+n)+\frac{1}{(m+n)}\right]=$

• A. 2
• B. -1
• C. 1
• D. 0

Answer 1

Answer: (A)

$\sec \theta =m,\tan \theta =n$
$\frac{1}{m}\left[(m+n)+\frac{1}{m+n}\right]$
$=\frac{1}{\sec \theta }\left[\sec \theta +\tan \theta +\frac{1}{\sec \theta +\tan \theta }\right]$
$=\frac{1}{\sec \theta }[\sec \theta +\tan \theta +\sec \theta -\tan \theta ]$
$=\frac{2\sec \theta }{\sec \theta }=2$