Question

If $\cos \theta =\frac{5}{13}$, where $\theta$ being an acute angle, then the value of $\frac{\cos \theta +5\cot \theta }{\text{cosec}\theta -\cos \theta }$ will be

• A. $\frac{169}{109}$
• B. $\frac{155}{109}$
• C. $\frac{385}{109}$
• D. $\frac{95}{109}$

Answer 1

Answer: (C)

$\frac{385}{109}$

Given, $\cos \theta =\frac{5}{13}$
Then $\sin \theta =\frac{12}{13}$
Hence, $\tan \theta =\frac{12}{5}$ and
$\text{cosec}\theta =\frac{13}{12}$
Substituting in the equation, we get
$=\frac{\frac{5}{13}+\frac{5.5}{12}}{\frac{13}{12}-\frac{5}{13}}$
$=\frac{5\left(12\right)+25\left(13\right)}{13\left(13\right)-5\left(12\right)}$
$=\frac{60+300+25}{169-60}$
$=\frac{385}{109}$