Question

If $5\cos \Theta =6\sin \Theta$; evaluate :

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

Answer 1

$5\cos \Theta =6\sin \Theta$
$\tan \Theta =\frac{5}{6}$
Now, $\frac{12\sin \Theta -3\cos \Theta }{12\sin \Theta +3\cos \Theta }$
Multiply and divide by $\cos \Theta$,
= $\frac{12\tan \Theta -3}{12\tan \Theta +3}$
= $\frac{12\left(\frac{5}{6}\right)-3}{12\left(\frac{5}{6}\right)+3}$
= $\frac{60-18}{60+18}$
= $\frac{42}{78}$
= $\frac{7}{13}$