`"If"sin{cot^(-1)(x+1)}=cos(tan^(-1)x),` then find `x.`

Explanation

To solve the equation \( \sin(\cot^{-1}(x+1)) = \cos(\tan^{-1}(x)) \), we will follow these steps:

### Step 1: Rewrite the Inverse Trigonometric Functions
We start by rewriting the left side using the identity for \( \sin(\cot^{-1}(y)) \) and the right side using the identity for \( \cos(\tan^{-1}(y)) \).

Using the identity:
- \( \sin(\cot^{-1}(y)) = \frac{y}{\sqrt{1+y^2}} \)
- \( \cos(\tan^{-1}(y)) = \frac{1}{\sqrt{1+y^2}} \)
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