Let `f(x)=2cos e c2x+secx+cos e cxdot` Then find the minimum value of `f(x)forx in (0,pi/2)dot`

Explanation

To find the minimum value of the function \( f(x) = 2 \csc(2x) + \sec(x) + \csc(x) \) for \( x \) in the interval \( (0, \frac{\pi}{2}) \), we can follow these steps:

### Step 1: Rewrite the function in terms of sine and cosine
We can express the function using sine and cosine:
\[ f(x) = 2 \csc(2x) + \sec(x) + \csc(x) = \frac{2}{\sin(2x)} + \frac{1}{\cos(x)} + \frac{1}{\sin(x)} \]
Using the identity \( \sin(2x) = 2 \sin(x) \cos(x) \), we can rewrite \( \csc(2x) \):
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