Given that sin a = 5/9, we can first find cos a using the Pythagorean identity sin^2 a + cos^2 a = 1.
sin^2 a + cos^2 a = 1(5/9)^2 + cos^2 a = 125/81 + cos^2 a = 1cos^2 a = 1 - 25/81cos^2 a = 56/81cos a = ±√(56/81)cos a = ±(√56)/9
Now we can substitute sin a = 5/9 and cos a = ±(√56)/9 into the expression:
81(1 - cos^2 a)81(1 - 56/81)81*(25/81)25
Given that sin a = 5/9, we can first find cos a using the Pythagorean identity sin^2 a + cos^2 a = 1.
sin^2 a + cos^2 a = 1
(5/9)^2 + cos^2 a = 1
25/81 + cos^2 a = 1
cos^2 a = 1 - 25/81
cos^2 a = 56/81
cos a = ±√(56/81)
cos a = ±(√56)/9
Now we can substitute sin a = 5/9 and cos a = ±(√56)/9 into the expression:
81(1 - cos^2 a)
81(1 - 56/81)
81*(25/81)
25