Question

3tan^2 (x) -1=0 the solutions of this equation over interval (0, ii) are

Answer 1

\[3\tan ^{2}x-1=0\]\[(\sqrt{3}tanx-1)(\sqrt{3}tanx+1)=0\]\[\sqrt{3}tanx-1=0\]\[\sqrt{3}tanx=1\]\[tanx=\frac{ 1 }{ \sqrt{3} }\]\[x=\tan^{-1} \frac{ 1 }{ \sqrt{3} }+ n \pi \]and \[\sqrt{3}tanx+1=0\]\[\sqrt{3}tanx=-1\]\[tanx=\frac{ -1 }{ \sqrt{3} }\]\[x=\tan^{-1} \frac{ -1 }{ \sqrt{3} }+n \pi\]