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 will follow these steps:

### Step 1: Simplify \(\cos(\frac{5\pi}{8})\) and \(\cos(\frac{7\pi}{8})\)

We know that:
- \(\cos(\frac{5\pi}{8}) = \cos(\pi - \frac{3\pi}{8}) = -\cos(\frac{3\pi}{8})\)
- \(\cos(\frac{7\pi}{8}) = \cos(\pi - \frac{\pi}{8}) = -\cos(\frac{\pi}{8})\)

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