Question

$\int \cos 2\theta .\ln \frac{\cos \theta +\sin \theta }{\cos \theta -\sin \theta }d\theta$

• A. $\frac{1}{2}ln\left(\frac{\cos \theta -\sin \theta }{\cos \theta +\sin \theta }\right)\sin 2\theta -\frac{1}{2}\ln \left(\sec 2\theta \right)+C$
  
• B. $\frac{1}{2}\ln \left(\frac{\cos \theta -\sin \theta }{\cos \theta +\sin \theta }\right)\sin 2\theta -\frac{1}{2}\ln \left(\text{cosec}2\theta \right)+C$
• C. $\frac{1}{2}\ln \left(\frac{\cos \theta +\sin \theta }{\cos \theta -\sin \theta }\right)\sin 2\theta -\frac{1}{2}\ln \left(\text{cosec}2\theta \right)+C$
• D. $\frac{1}{2}\ln \left(\frac{\cos \theta +\sin \theta }{\cos \theta -\sin \theta }\right)\sin 2\theta -\frac{1}{2}\ln \left(\sec 2\theta \right)+C$

Answer 1

The correct option is D $\frac{1}{2}\ln \left(\frac{\cos \theta +\sin \theta }{\cos \theta -\sin \theta }\right)\sin 2\theta -\frac{1}{2}\ln \left(\sec 2\theta \right)+C$

undefined