Question

Find the solutions of the equation if 0≤𝑡<2𝜋

tan^2 𝑡−1=0

Answer 1

$$\tan^2t-1=0$$

$$(\tan t-1)(\tan t+1)=0$$

$$\tan t=\pm1$$

$$t=\dfrac{\pi}{4}+\dfrac{\pi n}{2}, n\in \Z$$

If we consider $0\leq t<2\pi$

$$t_1=\dfrac{\pi}{4}, t_2=\dfrac{3\pi}{4}, t_3=\dfrac{5\pi}{4}, t_4=\dfrac{7\pi}{4}$$

$$\{\dfrac{\pi}{4}, \dfrac{3\pi}{4}, \dfrac{5\pi}{4}, \dfrac{7\pi}{4}\}$$