Question

If \[\tan \theta = \frac{4}{5}\] find the value of \[\frac{\cos \theta - \sin \theta}{\cos \theta + \sin \theta}\]

Answer 1

It is given that `tan θ=4/5` . 

We have to find  \[\frac{\cos \theta - \sin \theta}{\cos \theta + \sin \theta}\] 

\[\frac{\cos \theta - \sin \theta}{\cos \theta + \sin \theta}\]

= `1-( sinθ/cos θ)/(1+sinθ/cos θ)`    [Dividing both numberator and denominator by cos θ] 

=`(1-tanθ)/(1+ tan θ)` 

= `(1-4/5)/(1+4/5)` 

=`1/9`