If $ an heta=\frac{5}{12}$, then the value of $\frac{\sin heta+\cos heta}{\sin heta-\cos

Question

If $	an 	heta=\frac{5}{12}$, then the value of $\frac{\sin 	heta+\cos 	heta}{\sin 	heta-\cos 	heta}$ is :\

Professor PC Thomas Classes · Answer

(a): Given, $	an 	heta=\frac{5}{12}$\ $	herefore \frac{\sin 	heta+\cos 	heta}{\sin 	heta-\cos 	heta}=\frac{\frac{\sin 	heta}{\cos 	heta}+\frac{\cos 	heta}{\cos 	heta}}{\frac{\sin 	heta}{\cos 	heta}-\frac{\cos 	heta}{\cos 	heta}}$\ [ ∵ Dividing numerator and denominator by $\cos 	heta$ ]\ $=\frac{	an 	heta+1}{	an 	heta-1}$\ $=\frac{\frac{5}{12}+1}{\frac{5}{12}-1}$ $$ \left[\because 	an 	heta=\frac{5}{12}ight] $$ $$ =\frac{5+12}{5-12}=-\frac{17}{7} $$