Question

If $2\cot A=3$, find the value of : $\frac{5\sin A-2\cos A}{6\cos A+\sin A}$ is $\frac{1}{m}$, then m is

Answer 1

$2\cot A=3$
$\cot A=\frac{3}{2}$
or $\tan A=\frac{2}{3}$
Now, $\frac{5\sin A-2\cos A}{6\cos A+\sin A}$.
Multiply and Divide by $\cos A$
= $\frac{5\tan A-2}{6+\tan A}$
= $\frac{5\left(\frac{P}{B}\right)-2}{6+\frac{P}{B}}$
= $\frac{5\left(\frac{2}{3}\right)-2}{6+\frac{2}{3}}$
= $\frac{10-6}{18+2}$
= $\frac{4}{20}$
= $\frac{1}{5}$