Final answer:
The sum can be expressed as a product of sines and cosines: 2sin(5x)cos(-4x).
Step-by-step explanation:
To express the given sum as a product of sines and/or cosines, we can use the trigonometric identity:
sin(a) + sin(b) = 2sin((a+b)/2)cos((a-b)/2)
Applying this identity to the given sum, we have:
sin(x) + sin(9x) = 2sin((x+9x)/2)cos((x-9x)/2)
Simplifying,
sin(x) + sin(9x) = 2sin(5x)cos(-4x)
The given sum can be expressed as a product of sines and cosines as 2sin(5x)cos(-4x).