Prove that: `(1+cospi/8)(1+cos(3pi)/8)(1+cos(5pi)/8)(1+cos(7pi)/8)=1/8`

Explanation

To prove that \((1 + \cos \frac{\pi}{8})(1 + \cos \frac{3\pi}{8})(1 + \cos \frac{5\pi}{8})(1 + \cos \frac{7\pi}{8}) = \frac{1}{8}\), follow these steps:

### Step 1: Simplify the Cosine Terms
Rewrite the cosine terms using the identity \(\cos(\pi - \theta) = -\cos(\theta)\):
\[ \cos \frac{5\pi}{8} = \cos \left(\pi - \frac{3\pi}{8}\right) = -\cos \frac{3\pi}{8} \]
\[
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