Question

If $\cos A=5/13$, then what is the value of
$\frac{\sin A-\cot A}{2\tan A}$?

• A. $395/3644$
• B. $395/3844$
• C. $395/3744$
• D. $385/3744$

Answer 1

The correct option is C $395/3744$

$cosA=\frac{5}{13}\Rightarrow sinA=\sqrt{1-co{s}^{2}A}=\frac{12}{13}$

$\Rightarrow \frac{sinA-cotA}{2tanA}=\frac{sinA-\frac{cosA}{sinA}}{2\frac{sinA}{cosA}}$

$\Rightarrow \frac{12/13-\frac{5}{12}}{2\times \frac{12}{5}}=\frac{395}{3744}$