Final answer:
To express 8sin(37y)cos(18y) as a sum, we use the product-to-sum trigonometric identities, resulting in the expression 4sin(55y)+4sin(19y), which matches option c).
Step-by-step explanation:
The student is required to express 8sin(37y)cos(18y) as a sum. This can be achieved by using the trigonometric identity for the product-to-sum formulas, which states that sin a × cos b = \(\frac{1}{2}\)(sin(a + b) + sin(a - b)). Applying this to the given expression:
8sin(37y)cos(18y) = 8 * \(\frac{1}{2}\)(sin((37y + 18y)) + sin((37y - 18y)))
Therefore, it simplifies to:
4sin(55y) + 4sin(19y)
So, the correct answer is option c) 4sin(55y)+4sin(19y).