c.
\(\Leftrightarrow\left\{{}\begin{matrix}2x+1>0\\\left(2x+1\right)^2>\left(x+2\right)^2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x>-\dfrac{1}{2}\\x^2>1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x>-\dfrac{1}{2}\\\left[{}\begin{matrix}x>1\\x< -1\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow x>1\)
d.
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge0\\2-x< 0\end{matrix}\right.\\\left\{{}\begin{matrix}2-x\ge0\\x>\left(2-x\right)^2\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge0\\x>2\end{matrix}\right.\\\left\{{}\begin{matrix}x\le2\\x^2-5x+4< 0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x>2\\\left\{{}\begin{matrix}x\le2\\1< x< 4\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x>2\\1< x\le2\end{matrix}\right.\)
\(\Leftrightarrow x>1\)
2.
Do \(a\in\left(\dfrac{\pi}{2};\pi\right)\Rightarrow sina>0\)
\(\Rightarrow sina=\sqrt{1-cos^2a}=\sqrt{1-\left(-\dfrac{3}{5}\right)^2}=\dfrac{4}{5}\)
