To solve this problem, we need to use trigonometric identities and equations. Let's break down the steps to find the value of a b / c d:

Given equations:
1) cos A cos2 A = 1
2) a sin12 A b sin10 A c sin8 A d sin6 A - 1 = 0

Step 1: Simplifying the first equation
Using the identity cos2 A = 1 - sin2 A, we can rewrite the first equation as:
cos A (1 - sin2 A) = 1
cos A - cos A sin2 A = 1
cos A = 1 + cos A sin2 A

Step 2: Simplifying the second equation
Let's rewrite the second equation in terms of sin A using the identity sin2 A = 1 - cos2 A:
a sin12 A - b sin10 A + c sin8 A - d sin6 A = 1

Step 3: Using the double angle identity
Using the double angle identity sin 2A = 2sin A cos A, we can rewrite the first equation as:
cos A = 1 + 2sin A cos A sin2 A
cos A = 1 + 2sin A cos A (1 - cos2 A)
cos A = 1 + 2sin A cos A - 2sin A cos3 A

Step 4: Simplifying the equation system
Now, let's substitute the value of cos A from the first equation into the second equation:
a sin12 A - b sin10 A + c sin8 A - d sin6 A = 1 + 2sin A cos A - 2sin A cos3 A

Step 5: Rearranging the equation
Rearranging the equation, we get:
2sin A cos A - 2sin A cos3 A + a sin12 A - b sin10 A + c sin8 A - d sin6 A - 1 = 0

Step 6: Comparing coefficients
Comparing the coefficients of sin A and cos A in the equation, we have:
2cos A = a
-2cos3 A - b = 0
1 = c
-1 = d

Step 7: Finding the value of a b / c d
Now, we can calculate the value of a b / c d:
a = 2cos A = 2(1) = 2
b = -2cos3 A = -2(1)3 = -2
c = 1
d = -1

Therefore, a b / c d = (2)(-2) / (1)(-1) = 4 / 1 = 4

Hence, the correct answer is option 'B' (4).