Question

If $tan\theta =\frac{4}{5}$, find the value of $\frac{cos\theta -sin\theta }{cos\theta +sin\theta }$.

Answer 1

given $tan\left(\theta \right)=4/5$

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

[dividing with cos($\theta$) in numerator and denominator]

therefore now substituting the value we get

$\frac{1-4/5}{1+4/5}=\frac{1/5}{9/5}=\frac{1}{9}$

therefore the required value is $\frac{1}{9}$