Differentiate `tan^(-1){(cosx)/(1+sinx)}`,`0ltxltpi`

Explanation

To differentiate the function \( U = \tan^{-1}\left(\frac{\cos x}{1 + \sin x}\right) \), we will follow these steps:

### Step 1: Rewrite the function
We start with the function:
\[ U = \tan^{-1}\left(\frac{\cos x}{1 + \sin x}\right) \]

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