Question

tan^2 (x) - 3 =0 solve for 0° < x < 360°

Answer 1

Given the equation:

$\tan ^2x-3=0$

first let's move the -3 to the right side. Remember that when we do this, it must move with the opposite sign:

$\begin{gathered} \tan ^2x-3=0 \\ \Rightarrow\tan ^2x=3 \end{gathered}$

now we can apply the square root on both sides of the equation to get the following:

$\begin{gathered} \sqrt[]{\tan ^2x}=\sqrt[]{3} \\ \Rightarrow\tan x=\sqrt[]{3} \end{gathered}$

next we use the inverse function of tangent to solve for x:

$\begin{gathered} \tan x=\sqrt[]{3} \\ \Rightarrow x=\tan ^{-1}(\sqrt[]{3})=60 \\ x=60 \end{gathered}$

therefore, x = 60