Tg’2 -1=0

To solve the equation \( \tan^2(x) - 1 = 0 \), we can start by isolating \( \tan^2(x) \):

\[ \tan^2(x) = 1 \]

Taking the square root of both sides, we have:

\[ \tan(x) = 1 \quad \text{or} \quad \tan(x) = -1 \]

Now, we can find the general solutions for \( \tan(x) = 1 \) and \( \tan(x) = -1 \):

1. For \( \tan(x) = 1 \):

   • The solution is \( x = \frac{\pi}{4} + n\pi \), where \( n \) is any integer.

2. For \( \tan(x) = -1 \):

   • The solution is \( x = \frac{3\pi}{4} + n\pi \), where \( n \) is any integer.

So, the complete solution set for \( \tan^2(x) - 1 = 0 \) is:

\[ x = \frac{\pi}{4} + n\pi \quad \text{and} \quad x = \frac{3\pi}{4} + n\pi, \quad n \in \mathbb{Z} \]