`"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 inverse trigonometric functions in terms of sine and cosine.

- For \( \cot^{-1}(x+1) \):
\[
\cot^{-1}(x+1) = \theta \implies \cot(\theta) = x + 1 \implies \tan(\theta) = \frac{1}{x+1}
...