Question

The value of $\frac{1+\sin 2\theta +\cos 2\theta }{1+\sin 2\theta -\cos 2\theta }=$

Answer 1

We have,

$\frac{1+\sin 2\theta +\cos 2\theta }{1+\sin 2\theta -\cos 2\theta }$

Then,

$\frac{1+2\sin \theta \cos \theta +2{\cos }^2\theta -1}{1+2\sin \theta \cos \theta -1+2{\sin }^2\theta }$

$=\frac{2\sin \theta \cos \theta +2{\cos }^2\theta }{2\sin \theta \cos \theta +2{\sin }^2\theta }$

$=\frac{2\cos \theta (\sin \theta +\cos \theta )}{2\sin \theta (\cos \theta +\sin \theta )}$

$=\frac{\cos \theta }{\sin \theta }$

$=\cot \theta$

Hence, this is the answer.