Question

If $\tan \theta =\frac{5}{12}$, then $\sec \theta =$........

• A. $\frac{13}{12}$
• B. $\frac{12}{13}$
• C. $\frac{1}{5}$
• D. $\frac{5}{12}$

Answer 1

The correct option is A $\frac{13}{12}$

$\tan \theta =\frac{5}{12}$

$\Rightarrow {\tan }^2\theta =\frac{25}{144}$

$\Rightarrow {\sec }^2\theta -1=\frac{25}{144}$ $[\because 1+{\tan }^2\theta ={\sec }^2\theta ]$

$\Rightarrow {\sec }^2\theta =\frac{25}{144}+1$

$=\frac{25+144}{144}$

$\Rightarrow {\sec }^2\theta =\frac{169}{144}$

$\Rightarrow \sec \theta =\sqrt{\frac{169}{144}}=\frac{13}{12}$

Hence, the answer is $\frac{13}{12}.$