The value of
`(1+cos ""(2pi)/(15))(1+cos""(8pi)/(15))(1+cos""(12pi)/(15))is`

Options

A. `(3-sqrt5)/(16)`
B. `(3+sqrt5)/(16)`
C. `(3+sqrt5)/(8)`
D. `(3-sqrt5)/(8)`

Explanation

To solve the expression \( (1 + \cos \frac{2\pi}{15})(1 + \cos \frac{8\pi}{15})(1 + \cos \frac{12\pi}{15}) \), we can use trigonometric identities to simplify the terms.

### Step 1: Use the identity for cosine
Recall the identity:
\[ 1 + \cos x = 2 \cos^2 \left(\frac{x}{2}\right) \]
Using this identity, we can rewrite each term in the expression.
...