Question

$\frac{12sin\Theta -3cos\Theta }{12sin\Theta +3cos\Theta }$ is $\frac{7}{m}$, m is

Answer 1

$5\cos \Theta =6\sin \Theta$
$\frac{5}{6}=\frac{\sin \Theta }{\cos \Theta }$
$\tan \Theta =\frac{5}{6}$
Now, $\frac{12sin\Theta -3cos\Theta }{12sin\Theta +3cos\Theta }$
Multiply and divide by $\cos \Theta$
= $\frac{12\tan \Theta -3}{12tan\Theta +3}$
= $\frac{12\left(\frac{5}{6}\right)-3}{12\left(\frac{5}{6}\right)+3}$
= $\frac{10-3}{10+3}$
= $\frac{7}{13}$