Find the least value of `sec A+secB+secC` in an acute angled triangle

Explanation

To find the least value of \( \sec A + \sec B + \sec C \) in an acute-angled triangle, we can follow these steps:

### Step 1: Understand the relationship between secant and cosine
Recall that \( \sec A = \frac{1}{\cos A} \), \( \sec B = \frac{1}{\cos B} \), and \( \sec C = \frac{1}{\cos C} \). Therefore, we can express the sum as:
\[ \sec A + \sec B + \sec C = \frac{1}{\cos A} + \frac{1}{\cos B} + \frac{1}{\cos C} \]

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