Prove that `(sec^4alpha)/(tan^2beta)+(sec^4beta)/(tan^2alpha)ge8`. If each term in the expression is well defined.

Explanation

To prove that \(\frac{\sec^4 \alpha}{\tan^2 \beta} + \frac{\sec^4 \beta}{\tan^2 \alpha} \geq 8\), we will use the Cauchy-Schwarz inequality.

### Step-by-Step Solution:

1. **Rewrite the expression**:
We start with the expression:
\[
\frac{\sec^4 \alpha}{\tan^2 \beta} + \frac{\sec^4 \beta}{\tan^2 \alpha}
...