Use the product-to-sum formula to write the given product as a sum or difference. (attached)

the product to sum formula\[\sin A \sin B = -\frac{1}{2}\left( \cos \left( A + B \right) - \cos \left( A - B \right) \right)\]\[12 \sin \frac{\pi}{6} \sin \frac{\pi}{6} = -12\left( \frac{1}{2} \right)\left( \cos \left( \frac{\pi}{6} + \frac{\pi}{6} \right) - \cos \left( \frac{\pi}{6} - \frac{\pi}{6} \right)\right)\]

I don't think that that is one of my possible answers. Give me a minute and I'll give them to you.

you need to simplify it further

A. 6sin(π/12) B. 6 - 6cos(π/3) C. 6 + 6cos(π/12) D. -6sin(π/12) E. 6sin(π/6) + 6cos(π/6)

\[-6\left( \cos \frac{\pi}{3} - \cos 0\right) = 6 - 6 \cos \frac{\pi}{3}\]

Thank you! I really appreciate your help, especially that you showed me how you did it.

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