2.
\(\Leftrightarrow sin\left(\dfrac{x}{2}+10^0\right)=-\dfrac{1}{2}\)
\(\Leftrightarrow sin\left(\dfrac{x}{2}+10^0\right)=sin\left(-30^0\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{x}{2}+10^0=-30^0+k360^0\\\dfrac{x}{2}+10^0=210^0+k360^0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{x}{2}=-40^0+k360^0\\\dfrac{x}{2}=200^0+k360^0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-80^0+k720^0\\x=400^0+k720^0\end{matrix}\right.\)
5.
\(\Leftrightarrow cot\left(2x+\dfrac{5\pi}{2}\right)=-\dfrac{\sqrt{3}}{3}\)
\(\Leftrightarrow cot\left(2x+\dfrac{\pi}{2}+2\pi\right)=-\dfrac{\sqrt[]{3}}{3}\)
\(\Leftrightarrow cot\left(2x+\dfrac{\pi}{2}\right)=-\dfrac{\sqrt{3}}{3}\)
\(\Leftrightarrow tan2x=\dfrac{\sqrt{3}}{3}\)
\(\Leftrightarrow2x=\dfrac{\pi}{6}+k\pi\)
\(\Leftrightarrow x=\dfrac{\pi}{12}+\dfrac{k\pi}{2}\)
