Question

Find the general solution $\tan x=-1/\surd 3$.

Answer 1

Evaluate the given expression

$$\begin{gathered} \Rightarrow \tan \left(x\right)=-1/\sqrt{3} \\ \Rightarrow x={\tan }^{-1}\left(-1/\sqrt{3}\right)=-{\tan }^{-1}\left(\tan \frac{\mathrm{\pi }}{6}\right) \\ \Rightarrow x=-\frac{\mathrm{\pi }}{6} \end{gathered}$$

So, $x=n\mathrm{\pi }+\left(-\frac{\mathrm{\pi }}{6}\right)$ [$\mathbf{\because }\mathbf{}\mathit{\theta }\mathbf{=}\mathit{n}\mathbf{\pi }\mathbf{+}\mathbf{\alpha }$]

Hence, the general solution is$x=n\mathrm{\pi }-\frac{\mathrm{\pi }}{6}$.