Write each of the following in the simplest form:

(i)`tan^(-1){sqrt(1+x^2)-x},\ \ x in R`

(ii) `tan^(-1){(sqrt(1+x^2)-1)/x},\ \ x!=0`

Explanation

To simplify the given inverse trigonometric functions, we will follow a systematic approach for each part.

### (i) Simplifying \( \tan^{-1}(\sqrt{1+x^2} - x) \)

1. **Substitution**: Let \( x = \tan(\theta) \). Then, we have:
\[ \sqrt{1+x^2} = \sqrt{1+\tan^2(\theta)} = \sec(\theta) \]
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