QuestionProduct-to-Sum Formulas:
1. $\left.\sin (u) \cos (v)=\frac{1}{2}[\sin (u+v))+\sin (u-v)\right]$
2. $\left.\cos (u) \sin (v)=\frac{1}{2}[\sin (u+v))-\sin (u-v)\right]$
3. $\left.\cos (u) \cos (v)=\frac{1}{2}[\cos (u+v))+\cos (u-v)\right]$
4. $\left.\sin (u) \sin (v)=\frac{1}{2}[\cos (u-v))-\cos (u+v)\right]$
Rewrite the expression below using one of the given formulas. $$\sin (3 x) \sin (5 x)$$ Using formula number one: $$\sin (3 x) \sin (5 x)=\frac{1}{2}[\cos (3 x-5 x)-\cos (3 x+5 x)]$$ Using formula four: $$\sin (3 x) \sin (5 x)=\frac{1}{2}[\cos (3 x+5 x)-\cos (3 x-5 x)]$$ Using formula one: $$\sin (3 x) \sin (5 x)=\frac{1}{2}[\cos (3 x+5 x)-\cos (3 x-5 x)]$$ Using formula number four: $$\sin (3 x) \sin (5 x)=\frac{1}{2}[\cos (3 x-5 x)-\cos (3 x+5 x)]$$