If csc θ cot θ=a and csc θ−cot θ=1/a​, then prove that (a²−1)(sin θ cos θ)=(a−1)²−2.
A. a²−1=a−1
B. a²+2=a2−2
C. a²−1=2(a−1)
D. sin θ cos θ=a²−1