Question

Given : $\cos A=\frac{5}{13}$. If $\cot A+\frac{1}{\cos A}$ is $\frac{181}{m}$, $m$ is:

• A. $60$
• B. $12$
• C. $18$
• D. $55$

Answer 1

The correct option is A $60$

$\cos A=\frac{5}{13}$
$\cos A=\frac{B}{H}=\frac{5}{13}$
Using Pythagoras theorem,
$H^2=P^2+B^2$
${13}^2=P^2+5^2$
$169=P^2+25$
$P=12$
Now, $\cot A+\frac{1}{\cos A}=\cot A+\sec A$
= $\frac{B}{P}+\frac{H}{B}$
= $\frac{5}{12}+\frac{13}{5}$
= $\frac{25+156}{60}$
= $\frac{181}{60}$