`d/(dx){tan^(-1)((cosx)/(1+sinx))}e q u a l` `1/2` (b) `x` (c) `(1-x^2)/(1+x^2)` (d) `1`

Explanation

To differentiate the function \( y = \tan^{-1}\left(\frac{\cos x}{1 + \sin x}\right) \), we will apply the chain rule and the quotient rule. Let's go through the solution step by step.

### Step 1: Identify the function
We have:
\[ y = \tan^{-1}\left(\frac{\cos x}{1 + \sin x}\right) \]

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