With the help of graph find the solution set of inequation tanx>-√3

Hi Nakush,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{As} \tan \mathrm{x} \mathrm{is} \mathrm{a} \mathrm{periodic} \mathrm{function} \mathrm{with} \mathrm{period} \mathrm{\pi }. \mathrm{Hence} \mathrm{we} \mathrm{can} \mathrm{find} \mathrm{solution} \mathrm{in} \mathrm{any} \\ \mathrm{interval} \mathrm{of} \mathrm{length} \mathrm{\pi } \mathrm{and} \mathrm{then} \mathrm{add} \mathrm{n\pi } \mathrm{in} \mathrm{the} \mathrm{solution}. \\ \mathrm{Cosider} \mathrm{x}\in \left(-\frac{\mathrm{\pi }}{2}, \frac{\mathrm{\pi }}{2}\right) \\ \tan \mathrm{x}>-\sqrt{3} \\ \mathrm{We} \mathrm{know} \mathrm{that} \tan \left(-\frac{\mathrm{\pi }}{3}\right)=-\sqrt{3} \end{gathered}$$

$$\begin{gathered} \mathrm{From} \mathrm{graph} \mathrm{it} \mathrm{is} \mathrm{clear} \mathrm{that} \mathrm{tanx}>-\sqrt{3} , \mathrm{when} \\ \mathrm{x}\in \left(-\frac{\mathrm{\pi }}{3}, \frac{\mathrm{\pi }}{2}\right) \\ \mathbf{General}\mathbf{ }\mathbf{solution}\mathbf{ }\mathbf{will}\mathbf{ }\mathbf{be}\mathbf{ }\mathbf{x}\mathbf{\in }\left(\mathbf{-}\frac{\mathbf{\pi }}{\mathbf{3}}\mathbf{+}\mathbf{n\pi }\mathbf{,}\mathbf{ }\frac{\mathbf{\pi }}{\mathbf{2}}\mathbf{+}\mathbf{n\pi }\right)\mathbf{.} \end{gathered}$$

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