Q6 q15.) which of the following four statements establishes the identity?

A is incorrect. The identity is for the Sin( A - B). It is not for the Cos(A - B)

B is closer, but NOT the answer. The sign in the middle is incorrect, for one thing. For another Cos(pi/2) = 0,, so the answer would be cos(theta) using this formula.

C The sign is correct in C. The problem is that it is the wrong formula for Cos(theta - pi/2). C should go 
Cos(theta - pi/2) = cos(theta) cos(pi/2) + sin(theta)*sin(pi/2)

D. Looks like it's the correct answer. See the comment for C: The identity for C is actually correct for D.
Cos(theta)cos(pi/2) = 0 because cos(pi/2) =0
Sin(theta)*sin(pi/2) = Sin(theta) because Sin(pi/2) = 1

Answer D <<<<<< answer.