Final answer:
The product of cosines given does not directly correspond to a known product-to-sum identity without additional context or manipulation.
Step-by-step explanation:
The question asks to write the following product of cosines as a sum: -8cos5/6x * cos8/7x. This problem involves the use of trigonometric identities to transform a product into a sum. However, typically, the product-to-sum identities involve the product of cos A and cos B where A and B are different angles. In this case, the powers of cosine do not directly allow for a conversion into a sum using standard trigonometric identities. As such, without additional context or clarification implying a simplification or manipulation that would make such a conversion possible, this expression as given does not correspond to a known product-to-sum identity.