Question

If $5\cot \theta =12$, find the value of : $\csc \theta +\sec \theta$ is $3\frac{41}{m}$, m is

• A. $40$
• B. $60$
• C. $50$
• D. $13$

Answer 1

Answer: (B)

$60$

$5\cot \theta =12$
$\cot \theta =\frac{12}{5}$
$\cot \theta =\frac{B}{P}=\frac{12}{5}$
Using Pythagoras Theorem,
$H^2=P^2+B^2$
$H^2={12}^2+5^2$
$H=13$
Now, $\csc \theta +\sec \theta$
= $\frac{H}{P}+\frac{H}{B}$
= $\frac{13}{12}+\frac{13}{5}$
= $\frac{65+156}{60}$
= $\frac{221}{60}$
= $3\frac{41}{60}$