[tex]\bf sin(2\theta)-6sin(\theta)=0\\\\
-----------------------------\\\\
\textit{Double Angle Identities}
\\ \quad \\
\boxed{sin(2\theta)=2sin(\theta)cos(\theta)}
\\ \quad \\
cos(2\theta)=
\begin{cases}
cos^2(\theta)-sin^2(\theta)\\
1-2sin^2(\theta)\\
2cos^2(\theta)-1
\end{cases}
\\ \quad \\
tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}\\\\
-----------------------------\\\\[/tex]
[tex]\bf 2sin(\theta)cos(\theta)-6sin(\theta)=0\impliedby \textit{common factor}
\\\\\\
sin(\theta)[2cos(\theta)-6]=0\implies
\begin{cases}
sin(\theta)=0\\
\measuredangle \theta=sin^{-1}(0)\\
0,\pi ,2\pi \\
----------\\
2cos(\theta)-6=0\\
cos(\theta)=\frac{6}{2}\\
cos(\theta)=3\\
\measuredangle \theta=cos^{-1}(3)\\
none
\end{cases}[/tex]
the domain for sine and cosine are eithe -1 or 1 or in between, anything outside of that, like 3, is a value that won't give us an angle
