The period of frac{sin theta + sin 2theta}{co | vedclass

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(C) Let $f(	heta) = \frac{\sin 	heta + \sin 2	heta}{\cos 	heta + \cos 2	heta}$.Using the sum-to-product formulas $\sin A + \sin B = 2 \sin \left(

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$\frac{2\pi}{3}$

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(C) Let $f(	heta) = \frac{\sin 	heta + \sin 2	heta}{\cos 	heta + \cos 2	heta}$.Using the sum-to-product formulas $\sin A + \sin B = 2 \sin \left(\frac{A+B}{2}ight) \cos \left(\frac{A-B}{2}ight)$ and $\cos A + \cos B = 2 \cos \left(\frac{A+B}{2}ight) \cos \left(\frac{A-B}{2}ight)$:$f(	heta) = \frac{2 \sin \left(\frac{3	heta}{2}ight) \cos \left(\frac{	heta}{2}ight)}{2 \cos \left(\frac{3	heta}{2}ight) \cos \left(\frac{	heta}{2}ight)} = 	an \left(\frac{3	heta}{2}ight)$.The period of $	an(k	heta)$ is $\frac{\pi}{|k|}$.Here,$k = \frac{3}{2}$,so the period is $\frac{\pi}{3/2} = \frac{2\pi}{3}$.

The period of $\frac{\sin \theta + \sin 2\theta}{\cos \theta + \cos 2\theta}$ is

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