Question

If $\cot \theta =\frac{b}{a},$, then find the value of $\frac{\cos \theta +\sin \theta }{\cos \theta -\sin \theta }$

Answer 1

$\cot \theta =\frac{b}{a}$.....(given)

$\therefore \frac{\cos \theta +\sin \theta }{\cos \theta -\sin \theta }$

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

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

$=\frac{b/a+1}{b/a-1}$

$=\frac{b+a}{b-a}$