[tex]\bf \textit{Double Angle Identities}
\\ \quad \\
cos(2\theta)=
\begin{cases}
cos^2(\theta)-sin^2(\theta)\\
1-2sin^2(\theta)\\
\boxed{2cos^2(\theta)-1}
\end{cases}\\\\
-------------------------------\\\\
cos(2\theta)\implies 2cos^2(\theta)-1\qquad \theta=\frac{\pi }{3}\implies 2\left[ cos\left( \frac{\pi }{3} \right)\right]^2-1
\\\\\\
2\left[ \cfrac{1}{2} \right]^2-1\implies 2\cdot \cfrac{1}{4}-1\implies \cfrac{1}{2}-1\implies -\cfrac{1}{2}[/tex]
