Question

Given: $\cos A=\frac{5}{13}$. If $\frac{\sin A-\cot A}{2\tan A}$ is $\frac{m}{3744}$, $m$ is:

• A. 695
• B. 595
• C. 295
• D. 395

Answer 1

Answer: (D)

395

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