Prove that:
i) `tan^(-1)(sqrt(x)+sqrt(y))/(1-sqrt(xy))=tan^(-1)sqrt(x)+tan^(-1)sqrt(y)`
ii) `tan^(-1)(x+sqrt(x))/(1-x^(3//2))=tan^(-1)x+tan^(-1)sqrt(x)`
iii) `tan^(-1)(sinx)/(1+cosx)=x/2`

Explanation

To prove the given statements, we will use the properties of inverse trigonometric functions, particularly the formula:

\[ \tan^{-1}(a) + \tan^{-1}(b) = \tan^{-1}\left(\frac{a + b}{1 - ab}\right) \quad \text{if } ab < 1 \]

### i) Prove that

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