Examine whether following pair of functions are identical or not?
(i) `f(x)=(x^(2)-1)/(x-1)` and `g(x)=x+1`
(ii) `f(x)=sin^(2)x+cos^(2)x` and `g(x)=sec^(2)x-tan^(2)x`

Explanation

To determine whether the given pairs of functions are identical, we need to check if they have the same domain and range. Let's analyze each pair step by step.

### Part (i): Functions \( f(x) \) and \( g(x) \)

1. **Identify the functions**:
- \( f(x) = \frac{x^2 - 1}{x - 1} \)
- \( g(x) = x + 1 \)

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