Question

If $\tan \theta =\frac{5}{12}$, find the value of $\frac{\cos \theta +\sin \theta }{\cos \theta -\sin \theta }$

Answer 1

$\tan \theta =\frac{5}{12}$

$\frac{\cos \theta +\sin \theta }{\cos \theta -\sin \theta }=?$

Take $\cos \theta$ common from numerator and denominator.

$\frac{\cos \theta (1+\frac{\sin \theta }{\cos \theta })}{\cos \theta (1-\frac{\sin \theta }{\cos \theta })}$

$=\frac{1+\tan \theta }{1-\tan \theta }$

$=\frac{1+\frac{5}{12}}{1-\frac{5}{12}}$

$=\frac{17}{7}$