[tex]\bf 2sin(t)cos(t)-cos(t)+2sin(t)-1=0
\\\\\\\
[2sin(t)cos(t)+2sin(t)]\quad -\quad [cos(t)+1]=0\\
\left. \qquad \right.\uparrow \\
\textit{common factoring}
\\\\\\
2sin(t)[\underline{cos(t)+1}]\quad -\quad [\underline{cos(t)+1}]=0\\
\left. \qquad \qquad \right.\uparrow \qquad \qquad \qquad\qquad \uparrow \\
\left. \qquad \right.\textit{some more common factor}
[/tex]
[tex]\bf [cos(t)+1][2sin(t)-1]=0\implies
\begin{cases}
2sin(t)-1=0\\\\
sin(t)=\frac{1}{2}\\\\
\measuredangle t=sin^{-1}\left( \frac{1}{2} \right)\\\\
\measuredangle t=\frac{\pi }{6}\ ,\ \frac{5\pi }{6}\\
----------\\
cos(t)+1=0\\\\
cos(t)=-1\\\\
\measuredangle t=cos^{-1}(-1)\\\\
\measuredangle t=\pi
\end{cases}[/tex]
