Question

If $\cot \theta =\frac{21}{20}$, then find the value of $\frac{\cos \theta -\sin \theta }{\cos \theta +\sin \theta }$.

Answer 1

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

$=\frac{\cot \theta -1}{\cot \theta +1}$ ( by dividing $N^r$ and$D^r$ by $\sin \theta$ )

$=\frac{\frac{21}{20}-1}{\frac{21}{20}+1}$

$=\frac{21-20}{21+20}$

$=\frac{1}{41}$