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=(\pi)/(4) \\ \text{Also,} \\ x=\tan ^(-1)(-1) \\ x=-(\pi)/(4) \end{gathered}`

The correct answer is option B, which is

`(\pi)/(4)`