Question

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

Answer 1

$5\cos \Theta =3$
$\cos \Theta =\frac{3}{5}$
Now, $\frac{cosec\Theta -cot\Theta }{cosec\Theta +cot\Theta }$
= $\frac{1-\cos \Theta }{1+\cos \Theta }$
= $\frac{1-\frac{3}{5}}{1+\frac{3}{5}}$
= $\frac{5-3}{5+3}$
= $\frac{2}{8}$
= $\frac{1}{4}$