[tex]\tan ^2x-1=0[/tex]
Factorizing the left expression using difference of two squares,
[tex]\tan ^2x-1^2=0[/tex][tex](\tan x+1)(\tan x-1)=0_{}[/tex][tex]\tan x+1=0\text{ or tanx-1=0}[/tex][tex]\begin{gathered} \tan x=-1\text{ or tanx=1} \\ x=\tan ^{-1}(-1)orx=\tan ^{-1}(1) \end{gathered}[/tex][tex]x=-45^0orx=45^0[/tex]
Hence from the given options, the value of x is 45°.
Option A is the correct answer.
