Question

In a right - angled triangle, it is given that $A$ is an acute angle and $\tan A=\frac{5}{12}$, then the value of $\frac{\cos A+\sin A}{\cos A-\sin A}$ is $m\frac{3}{7}$, where the value of m is

Answer 1

$\tan A=\frac{5}{12}$
$\tan A=\frac{P}{B}=\frac{5}{12}$
$P=5,B=12$
Now, $H^2=P^2+B^2$
$H^2=5^2+{12}^2$
$H^2=169$
$H=13$
$\cos A=\frac{B}{H}=\frac{12}{13}$
$\sin A=\frac{P}{H}=\frac{5}{13}$
$\frac{\sin A+\cos A}{\cos A-\sin A}=\frac{\frac{5}{13}+\frac{12}{13}}{\frac{12}{13}-\frac{5}{13}}$
= $\frac{5+12}{12-5}$
= $\frac{17}{7}$
= $2\frac{3}{7}$