Question

tan^2x-1=0

Answer 1

\[\tan^2(x)-1=0\]


\[\tan^2(x)=1\]


\[\tan(x)=\pm\sqrt{1}\]


\[\tan(x)=\sqrt{1} \ \textrm{or} \ \tan(x)=-\sqrt{1}\]


\[\tan(x)=1 \ \textrm{or} \ \tan(x)=-1\]


\[x=\arctan(1) \ \textrm{or} \ x=arctan(-1)\]


\[x=\frac{\pi}{4}+\pi n \ \textrm{or} \ x=\frac{3\pi}{4} +\pi n, x=-\frac{\pi}{4}+\pi n \ \textrm{or} \ x=-\frac{3\pi}{4} +\pi n\]


These solutions can be combined into the following


\[x=\frac{\pi n}{2}-\frac{\pi}{4}\]