Question

Find the value of $\frac{\cos \theta +\sin \theta }{\cos \theta -\sin \theta }$.

• A. $\tan (\frac{\pi }{4}+\theta )$
• B. $\tan (\frac{\pi }{4}-\theta )$
• C. $\cot (\frac{\pi }{4}+\theta )$
• D. $\cot (\theta -\frac{\pi }{4})$

Answer 1

The correct option is A $\tan (\frac{\pi }{4}+\theta )$

Take $\cos \theta$ common

$⟹\frac{1+\tan \theta }{1-\tan \theta }$

put $1=\tan \frac{\pi }{4}$

$⟹\frac{\tan \frac{\pi }{4}+\tan \theta }{1-\tan \frac{\pi }{4}\tan \theta }$

$⟹\tan (\frac{\pi }{4}+\theta )$