Question

Given: $\cos A=\frac{5}{13}$, then the value of

$\frac{\sin A-\cot A}{2\tan A}$ is $\frac{m}{3744}$

, where 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, $\frac{\sin A-\cot A}{2\tan A}$
= $\frac{\frac{12}{13}-\frac{5}{12}}{2\left(\frac{12}{5}\right)}$
= $\frac{\frac{144-65}{156}}{\frac{24}{5}}$
= $\frac{\frac{79}{156}}{\frac{24}{5}}$
= $\frac{395}{3744}$