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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 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`
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