The general solution of any trigonometric equation is given as:

$$ \[sin\text{ }x\text{ }=\text{ }sin\text{ }y\]

Or,

\[x\text{ }=\text{ }n\pi \text{ }+\text{ }{{\left( \text{ }1 \right)}^{n~}}y\] , where n ∈ Z.

\[cos\text{ }x\text{ }=\text{ }cos\text{ }y,\]

or,

\[x\text{ }=\text{ }2n\pi ~\pm ~y,\] where n ∈ Z.

\[tan\text{ }x\text{ }=\text{ }tan\text{ }y,\]

or,

\[x\text{ }=\text{ }n\pi ~+\text{ }y,\] where n ∈ Z.

\[\left( \mathbf{i} \right)~sin\text{ }x\text{ }=\text{ }1/2~~~~~~\]

As,  \[sin\text{ }{{30}^{o}}~=\text{ }sin\text{ }\pi /6\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\]

Hence,

\[Sin\text{ }x\text{ }=\text{ }sin\text{ }\pi /6\]

∴ the general solution is

\[x\text{ }=\text{ }n\pi \text{ }+\text{ }{{\left( \text{ }1 \right)}^{~n~}}\pi /6,\]

where n ∈ Z.

[as,

\[sin\text{ }x\text{ }=\text{ }sin\text{ }A\]

\[=>\text{ }x\text{ }=\text{ }n\pi \text{ }+\text{ }{{\left( \text{ }1 \right)}^{~n}}~A]\]

\[\left( \mathbf{ii} \right)~cos\text{ }x\text{ }=\text{ }\text{ }\surd 3/2\]

as, \[cos\text{ }{{150}^{o}}~=\text{ }\left( -\text{ }\surd 3/2 \right)\text{ }=\text{ }cos\text{ }5\pi /6\]

Hence,

\[Cos\text{ }x\text{ }=\text{ }cos\text{ }5\pi /6\]

∴ the general solution is

\[x\text{ }=\text{ }2n\pi ~\pm \text{ }5\pi /6\] , where n ϵ Z.