Question

prove that cos theta + cos (120 + theta) +cos(240 + theta) = 0

Answer 1

formula used in 2nd step is cosC + cosD=2cosC+D/2×cos C-D/2

Answer 2

$\begin{aligned}\cos \theta &+\cos (120+\theta)+\cos (240+\theta)=0 \\\cos \theta &+2 \cos \left(\frac{240+120+2 \theta)}{2} \cdot \cos \frac{(240+\theta-120-\theta)}{2}=0\right.\\\cos \theta+2 \cos \frac{(360+20)}{2} \cdot \cos \frac{(120)}{2} \\\cos \theta+2 \cos (180+\theta) \cdot \cos 60^{\circ} \\\cos \theta+2 \cos (180+\theta) \cdot \frac{1}{2} \\\cos \theta &+2 x-\cos \theta \times \frac{1}{2} \\& \cos \theta-\cos \theta=0\end{aligned}$

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