cos(5x/9) cos(13x/9) - sin(5x/9) sin(13x/9)
Using the identity cos(a)cos(b) - sin(a)sin(b) = cos(a + b):
= cos((5x/9) + (13x/9))= cos(18x/9)= cos(2x)
Therefore, the expression simplifies to cos(2x).
cos(5x/9) cos(13x/9) - sin(5x/9) sin(13x/9)
Using the identity cos(a)cos(b) - sin(a)sin(b) = cos(a + b):
= cos((5x/9) + (13x/9))
= cos(18x/9)
= cos(2x)
Therefore, the expression simplifies to cos(2x).