1. **State the problem:** We need to find how many solutions the equation $$\tan^2 x = 1$$ has. 2. **Recall the formula and properties:** The equation $$\tan^2 x = 1$$ means $$\tan x = \pm 1$$. 3. **Solve for $$x$$:** $$\tan x = 1 \implies x = \frac{\pi}{4} + k\pi, \quad k \in \mathbb{Z}$$ $$\tan x = -1 \implies x = -\frac{\pi}{4} + k\pi, \quad k \in \mathbb{Z}$$ 4. **Count solutions in one period:** The period of $$\tan x$$ is $$\pi$$, so in one period $$[0, \pi)$$: - $$\tan x = 1$$ at $$x = \frac{\pi}{4}$$ - $$\tan x = -1$$ at $$x = \frac{3\pi}{4}$$ (since $$-\frac{\pi}{4} + \pi = \frac{3\pi}{4}$$) Thus, there are 2 solutions in one period. 5. **Answer:** The number of solutions to $$\tan^2 x = 1$$ in one period is **2**. Therefore, the correct choice is **B. 2 solutions**.