Question

If $5\cos \Theta =3$,
$\frac{cosec\Theta -\cot \Theta }{cosec\Theta +\cot \Theta }$ is $\frac{1}{m}$, m is

Answer 1

$5\cos \Theta =3$
$\cos \Theta =\frac{3}{5}$
$\cos \Theta =\frac{B}{H}=\frac{3}{5}$
Using Pythagoras Theorem,
$H^2=P^2+B^2$
$5^2=P^2+3^2$
$P=4$
Now, $\frac{cosec\Theta -\cot \Theta }{cosec\Theta +\cot \Theta }$
= $\frac{\frac{H}{P}-\frac{B}{P}}{\frac{H}{P}+\frac{B}{P}}$
= $\frac{\frac{5}{4}-\frac{3}{4}}{\frac{5}{4}+\frac{3}{4}}$
= $\frac{5-3}{5+3}$
= $\frac{2}{8}$
= $\frac{1}{4}$