Evaluate:
(i) `inttan^(-1)((sin2x)/(1+cos2x))\ dx`
(ii) `intcos^(-1)(sinx)\ dx`

Explanation

Let's solve the given integrals step by step.

### (i) Evaluate \( \int \tan^{-1}\left(\frac{\sin 2x}{1 + \cos 2x}\right) \, dx \)

1. **Simplify the Expression**:
We start with the expression \( \frac{\sin 2x}{1 + \cos 2x} \).
Using the double angle identities, we know:
\[
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