To simplify the expression, we use the trigonometric identity:
cos(A)cos(B) + sin(A)sin(B) = cos(A - B)
In this case, A = 4π/9 and B = 5π/18. Therefore, the expression simplifies to:
cos(4π/9 - 5π/18) = cos(8π/18 - 5π/18) = cos(3π/18) = cos(π/6) = √3/2
So, the simplified expression is √3/2.
To simplify the expression, we use the trigonometric identity:
cos(A)cos(B) + sin(A)sin(B) = cos(A - B)
In this case, A = 4π/9 and B = 5π/18. Therefore, the expression simplifies to:
cos(4π/9 - 5π/18) = cos(8π/18 - 5π/18) = cos(3π/18) = cos(π/6) = √3/2
So, the simplified expression is √3/2.