The value of frac{sin theta + sin 3 theta}{co | vedclass

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(C) We use the sum-to-product formulas: $\sin A + \sin B = 2 \sin \frac{A+B}{2} \cos \frac{A-B}{2}$ and $\cos A + \cos B = 2 \cos \frac{A+B}{2} \cos \

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$	an 2 	heta$

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(C) We use the sum-to-product formulas: $\sin A + \sin B = 2 \sin \frac{A+B}{2} \cos \frac{A-B}{2}$ and $\cos A + \cos B = 2 \cos \frac{A+B}{2} \cos \frac{A-B}{2}$.Applying these to the expression:$\frac{\sin 	heta + \sin 3 	heta}{\cos 	heta + \cos 3 	heta} = \frac{2 \sin \frac{	heta + 3 	heta}{2} \cos \frac{	heta - 3 	heta}{2}}{2 \cos \frac{	heta + 3 	heta}{2} \cos \frac{	heta - 3 	heta}{2}}$$= \frac{2 \sin 2 	heta \cos(-	heta)}{2 \cos 2 	heta \cos(-	heta)}$Since $\cos(-	heta) = \cos 	heta$, we have:$= \frac{\sin 2 	heta}{\cos 2 	heta} = 	an 2 	heta$.

The value of $\frac{\sin \theta + \sin 3 \theta}{\cos \theta + \cos 3 \theta}$ is

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