Question

Which of the following are solutions to the equation tan2x-1 = 0? Check allthat apply.

Answer 1

Given the equation;

$\tan ^2x-1=0$

Add 1 to both sides of the equation and you'll have;

$\begin{gathered} \tan ^2x-1+1=0+1 \\ \tan ^2x=1 \end{gathered}$

Square root both sides and you'll have;

$\begin{gathered} \tan x=\pm\sqrt[]{1} \\ \tan x=\pm1 \\ \text{Therefore,} \\ x=\tan ^{-1}(1) \\ x=\frac{\pi}{4} \\ \text{Also,} \\ x=\tan ^{-1}(-1) \\ x=-\frac{\pi}{4} \end{gathered}$

The correct answer is option B, which is

$\frac{\pi}{4}$