Equation in tangent squared

Statement

Solve the trigonometric equation: $\tan^2 x - 1 = 0$

Solution

The equation splits into two elementary equations: $\tan^2 x = 1 \iff \tan x = 1 \ \vee\ \tan x = -1.$ From $\tan x = 1$ we get $x = \dfrac{\pi}{4} + k\pi$; from $\tan x = -1$ we get $x = -\dfrac{\pi}{4} + k\pi$. The two families can be combined: $\boxed{\,x = \frac{\pi}{4} + k\frac{\pi}{2},\quad k\in\mathbb{Z}.}$

Links

Topics: Trigonometric equations
Concepts: Elementary equation · Substitution
Functions: Tangent
Skills: Solving equations · Using formulae
Exercise type: Solving an equation