Question:
If $\tan \theta=\frac{4}{5}$, find the value of $\frac{\cos \theta-\sin \theta}{\cos \theta+\sin \theta}$.
Solution:
It is given that $\tan \theta=\frac{4}{5}$.
We have to find $\frac{\cos \theta-\sin \theta}{\cos \theta+\sin \theta}$.
$\frac{\cos \theta-\sin \theta}{\cos \theta+\sin \theta}$
$=\frac{1-\frac{\sin \theta}{\cos \theta}}{1+\frac{\sin \theta}{\cos \theta}}$ [Dividing both numerator and denominator by $\cos \theta$ ]
$=\frac{1-\tan \theta}{1+\tan \theta}$
$=\frac{1}{9}$