\[\left( \mathbf{v} \right)~tan\text{ }x\text{ }=\text{ }-1/\surd 3\]

Or,

\[tan\text{ }x\text{ }=\text{ }-1/\surd 3\]

or,

\[tan\text{ }x\text{ }=\text{ }tan\text{ }\left( \pi /6 \right)\]

\[=\text{ }tan\text{ }\left( -\pi /6 \right)\]

\[\left[ as,\text{ }tan\text{ }\left( -x \right)\text{ }=\text{ }-tan\text{ }x \right]\]

∴ the general solution is

\[x\text{ }=\text{ }n\pi \text{ }+\text{ }\left( -\pi /6 \right),\]

where n ϵ Z.

\[or\text{ }x\text{ }=\text{ }n\pi \text{ }\text{ }\pi /6,\]

where n ϵ Z.

\[\left( \mathbf{vi} \right)~\surd 3\text{ }sec\text{ }x\text{ }=\text{ }2\]

or,

\[sec\text{ }x\text{ }=\text{ }2/\surd 3\]

\[1/cos\text{ }x\text{ }=\text{ }2/\surd 3\]

\[Cos\text{ }x\text{ }=\text{ }\surd 3/2\]

\[=\text{ }cos\text{ }\left( \pi /6 \right)\]

∴ the general solution is

\[x\text{ }=\text{ }2n\pi ~\pm \text{ }\pi /6,\]

where n ϵ Z.