We can simplify the given expression as follows:
(sin(2π + 5x) + sin(-15x - π)) / (sin(π/2 + 10x) + 1)= (sin(5x) + sin(-15x)) / (cos(10x) + 1)= (sin(5x) - sin(15x)) / (cos(10x) + 1)= (-2sin(5x)cos(5x)) / (cos(10x) + 1)= -2sin(5x) / (cos(10x) + 1)
Therefore, the simplified expression is -2sin(5x) / (cos(10x) + 1).
We can simplify the given expression as follows:
(sin(2π + 5x) + sin(-15x - π)) / (sin(π/2 + 10x) + 1)
= (sin(5x) + sin(-15x)) / (cos(10x) + 1)
= (sin(5x) - sin(15x)) / (cos(10x) + 1)
= (-2sin(5x)cos(5x)) / (cos(10x) + 1)
= -2sin(5x) / (cos(10x) + 1)
Therefore, the simplified expression is -2sin(5x) / (cos(10x) + 1).