Prove each of the following identities :
`(i) (1+ cos theta + sin theta)/(1+ cos theta - sin theta) =(1+ sin theta)/(cos theta) `
`(ii) (sin theta + 1- cos theta)/(cos theta - 1 + sin theta) = (1+ sin theta)/(cos theta) `

Explanation

To prove the given trigonometric identities, we will start with the left-hand side (LHS) of each identity and manipulate it to show that it equals the right-hand side (RHS).

### Identity (i)
**Prove:**
\[ \frac{1 + \cos \theta + \sin \theta}{1 + \cos \theta - \sin \theta} = \frac{1 + \sin \theta}{\cos \theta} \]

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