Prove the identity: $\dfrac{1}{2} \left(\cos t + \sqrt{3} \sin t\right) = \cos \left(\dfrac{\pi}{3} - t\right)$
$\begin{aligned}
LHS & = \dfrac{1}{2} \left(\cos t + \sqrt{3} \sin t\right) \\\\
& = \dfrac{1}{2} \cos t + \dfrac{\sqrt{3}}{2} \sin t \\\\
& = \cos \dfrac{\pi}{3} \cos t + \sin \dfrac{\pi}{3} \sin t \\\\
& = \cos \left(\dfrac{\pi}{3} - t\right) = RHS
\end{aligned}$
Hence proved.