The value of `cos(1/2cos^(-1)(1/8))` is (a)`3/4` (b) `-3/4` (c) `1/(16)` (d) `1/4`

Explanation

To solve the problem \( \cos\left(\frac{1}{2} \cos^{-1}\left(\frac{1}{8}\right)\right) \), we will follow these steps:

### Step 1: Let \( \theta = \frac{1}{2} \cos^{-1}\left(\frac{1}{8}\right) \)
We start by defining \( \theta \) as half of the angle whose cosine is \( \frac{1}{8} \).

### Step 2: Express \( \cos^{-1}\left(\frac{1}{8}\right) \) in terms of \( \theta \)
From our definition, we have:
\[
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