Solve that following equations : `sec x cos 5x+1=0,` `0 lt x le pi/2` find the value of x

Explanation

To solve the equation \( \sec x \cos 5x + 1 = 0 \) for \( 0 < x \leq \frac{\pi}{2} \), we can follow these steps:

### Step 1: Rewrite the equation
Starting with the given equation:
\[ \sec x \cos 5x + 1 = 0 \]
We can isolate the term involving secant:
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