The value of x that satisfies `tan^(-1)(tan -3)=tan^(2)x` is

Options

A. `(pi)/(3)`
B. `-(pi)/(3)`
C. `sqrt(tan^(-1)3)`
D. `none of these

Explanation

To solve the equation \( \tan^{-1}(\tan(-3)) = \tan^2(x) \), we will proceed step by step.

### Step 1: Simplifying the left-hand side
We start by simplifying \( \tan^{-1}(\tan(-3)) \). We know that:
\[ \tan^{-1}(\tan(-\theta)) = -\theta + n\pi \quad \text{for } n \in \mathbb{Z} \]
In this case, we can express \( -3 \) as \( -3 + \pi \) since \( \tan^{-1} \) is periodic with a period of \( \pi \). Thus:
...