If sin (x) = 1/3 and sec (y) = 25/24, where x and y lie between 0 and π/2, evaluate the expression using trigonometric identities. (Enter an exact answer.) sin (x - y)

sin (x-y) = (24-14*sqrt (2)) / 75 Write down what you know sin (x) = 1/3 sec (y) = 25/24 cos (y) = 1/sec (y) = 24/25 cos (x) = sqrt (1-sin (x) ^2) = sqrt (1-1/9) = sqrt (8/9) = 2*sqrt (2) / 3 sin (y) = sqrt (1-cos (y) ^2) = sqrt (1-576/625) = sqrt (49/625) = 7/25 We now know the sin and cos of both x and y. Now to get the sin of x-y. sin (x-y) = sin (x) cos (y) - cos (x) sin (y) Substitute the known values for sin and cos of x and y, then evaluate and simplify sin (x-y) = (1/3) (24/25) - (2*sqrt (2) / 3) (7/25) sin (x-y) = 24/75 - 14*sqrt (2) / 75 sin (x-y) = (24-14*sqrt (2)) / 75