Question

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

Answer 1

$2\cot A=3$
$\cot A=\frac{3}{2}$
or $\tan A=\frac{2}{3}$
Now, $\frac{5sinA-2cosA}{6cosA+sinA}$
Multiply and divide by $\cos A$
$\frac{5tanA-2}{6+tanA}$
= $\frac{5\left(\frac{2}{3}\right)-2}{6+\frac{2}{3}}$
= $\frac{10-6}{18+2}$
= $\frac{4}{20}$
= $\frac{1}{5}$