`(sec8A-1)/(sec4A-1)` is equal to (A) `(tan2A)/(tan8A)` (B) `(tan8A)/(tan2A)` (C) `(cot8A)/(cot2A)` (D) none of these

Explanation

To solve the expression \((\sec 8A - 1) / (\sec 4A - 1)\), we can follow these steps:

### Step 1: Rewrite secant in terms of cosine
We know that \(\sec \theta = \frac{1}{\cos \theta}\). Therefore, we can rewrite the expression as follows:
\[ \frac{\sec 8A - 1}{\sec 4A - 1} = \frac{\frac{1}{\cos 8A} - 1}{\frac{1}{\cos 4A} - 1} \]

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