Mathematics - Functions Question with Solution | TestHub

$\begin{array}{rl}& \frac{\sin \theta +\sin 2\theta }{\cos \theta +\cos 2\theta }=\frac{2\sin \left(\frac{3\theta }{2}\right)\cos \left(\frac{\theta }{2}\right)}{2\cos \left(\frac{3\theta }{2}\right)\cos \left(\frac{\theta }{2}\right)}=\tan \left(\frac{3\theta }{2}\right)\\ & \text{Hence period }=\frac{2\pi }{3}\end{array}$