Solve the equation, `1+secx = 8tan^(2)(x/2)`

Explanation

To solve the equation \(1 + \sec x = 8 \tan^2\left(\frac{x}{2}\right)\), we will follow these steps:

### Step 1: Rewrite the equation using trigonometric identities
We know that:
\[ \tan^2\left(\frac{x}{2}\right) = \frac{1 - \cos x}{1 + \cos x} \]
Substituting this into the equation gives:
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