Given: cos A * cos2 A = 1

To find: a sin12 A * b sin10 A * c sin8 A * d sin6 A - 1 = 0

Solution:
Let's simplify the given equation step by step.

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

Step 2: Distributing cos A, we get:
cos A - cos A * sin2 A = 1

Step 3: Rearranging the terms, we have:
cos A = 1 + cos A * sin2 A

Step 4: Dividing both sides by cos A, we get:
1 = sec A + sin2 A

Step 5: Using the identity sec A = 1/cos A, we can rewrite the equation as:
1 = 1/cos A + sin2 A

Step 6: Multiplying both sides by cos A, we get:
cos A = 1 + cos A * sin2 A

Step 7: Rearranging the terms, we have:
cos A = 1 + cos A * sin2 A

Now, let's solve the given expression a sin12 A * b sin10 A * c sin8 A * d sin6 A - 1 = 0.

Step 1: Substitute sin2 A = 1 - cos2 A in the expression:
a sin12 A * b sin10 A * c sin8 A * d sin6 A - 1 = 0
a sin12 A * b sin10 A * c sin8 A * d sin6 A - 1 = a sin12 A * b sin10 A * c sin8 A * d (1 - cos2 A) - 1 = 0

Step 2: Substitute cos A = 1 + cos A * sin2 A from the previous equation:
a sin12 A * b sin10 A * c sin8 A * d (1 - cos2 A) - 1 = a sin12 A * b sin10 A * c sin8 A * d (1 - (1 + cos A * sin2 A)) - 1 = 0

Step 3: Simplifying further:
a sin12 A * b sin10 A * c sin8 A * d (1 - 1 - cos A * sin2 A) - 1 = 0
a sin12 A * b sin10 A * c sin8 A * d (-cos A * sin2 A) - 1 = 0

Step 4: Using the identity sin2 A = 1 - cos2 A, we can rewrite the equation as:
a sin12 A * b sin10 A * c sin8 A * d (-cos A * (1 - cos2 A)) - 1 = 0
a sin12 A * b sin10 A * c sin8 A * d (-cos A + cos3 A) - 1 = 0

Step 5: Simplifying further:
-a b c d cos A + a b c d cos3 A - 1 = 0

Step 6: Rearranging the terms, we have:
a b c d cos3 A - a b c d cos A - 1 =