If `sec(theta+alpha)+sec(theta-alpha)=2\ s e ctheta,` prove that `costheta=+-sqrt(2)cosalpha/2dot`

Explanation

To prove that \( \cos \theta = \pm \sqrt{2} \cos \frac{\alpha}{2} \) given that \( \sec(\theta + \alpha) + \sec(\theta - \alpha) = 2 \sec \theta \), we can follow these steps:

### Step 1: Rewrite the given equation
We start with the equation:
\[ \sec(\theta + \alpha) + \sec(\theta - \alpha) = 2 \sec \theta \]
This can be rewritten using the identity \( \sec x = \frac{1}{\cos x} \):
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