The value of `(1+cospi/8)(1+cos(3pi)/8)(1+cos(5pi)/8)(1+cos(7pi)/8)i s` (a)1/4 (b) 3/4 (c) 1/8 (d) 3/8

Explanation

To solve the expression \((1 + \cos \frac{\pi}{8})(1 + \cos \frac{3\pi}{8})(1 + \cos \frac{5\pi}{8})(1 + \cos \frac{7\pi}{8})\), we can simplify it step by step.

### Step 1: Rewrite Cosine Terms
We start by rewriting the cosine terms:
- \(\cos \frac{5\pi}{8} = \cos(\pi - \frac{3\pi}{8}) = -\cos \frac{3\pi}{8}\)
- \(\cos \frac{7\pi}{8} = \cos(\pi - \frac{\pi}{8}) = -\cos \frac{\pi}{8}\)

Thus, we can rewrite the expression as:
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