Question

Given : $5\cos A-12\sin A=0$; evaluate :
$\frac{\sin A+\cos A}{2\cos A-\sin A}$ is $\frac{17}{m}$, m is

Answer 1

$5\cos A-12\sin A=0$

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

Now, $\frac{\sin A+\cos A}{2\cos A-\sin A}$

Multiply and divide by $\cos A$

= $\frac{\tan A+1}{2-\tan A}$

= $\frac{\frac{5}{12}+1}{2-\frac{5}{12}}$

= $\frac{\frac{5+12}{12}}{\frac{24-5}{12}}$

= $\frac{17}{19}$