Step 1: Test with a value:
Take $A = 30^\circ$. Then $\sin 90^\circ = 1$, $\sin 30^\circ = \tfrac12$, so the first term is $1/(1/4) = 4$.
Step 2: Second term:
$\cos 90^\circ = 0$, so the second term is $0$. The expression equals $4$.
Step 3: Match:
$\cos 2A = \cos 60^\circ = \tfrac12$, and $8\cos2A = 4$. Other options give $0.5$, $\tfrac1{16}$ or $\tfrac{\sqrt3}{4}$, which differ, so option (B).
Final Answer:
The result is 8 cos 2A.
\[ \boxed{\text{(B) }8\cos 2A} \]