Question

Given: $\cos A=\frac{5}{13}$

evaluate: $\cot A+\frac{1}{\cos A}$ is $\frac{m}{60}$, m is

Answer 1

Given, $\cos A=\frac{5}{13}$
$\cos A=\frac{B}{H}=\frac{5}{13}$
Now, using Pythagoras Theorem,
$H^2=P^2+B^2$
${13}^2=P^2+5^2$
$P=12$
Now, $\cot A+\frac{1}{\cos A}$
= $\frac{B}{P}+\frac{1}{\frac{B}{H}}$
= $\frac{5}{12}+\frac{1}{\frac{5}{13}}$
= $\frac{5}{12}+\frac{13}{5}$
= $\frac{25+156}{60}$
= $\frac{181}{60}$