Use the given information to find the exact value

Question

cos A=(1/3), 0 < A < (π/2); sin B = - (1/2), (πi/2) < B < 2π,

Find sin (A-B)

a. 2 √6 + 1 / 6

b. √3 + 2 √2 / 6

c. √3 - 2 √2 / 6

d. 2 √6 - 1 / 6

Answer 1

cos A = 1/3, sin A = (2√2) / 3

sin B = -1/2, cos B = -√3 / 3

sin (A - B) = sin A cos B - cos A sin B

Substitute values and simplify