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Question Number 140114 by EnterUsername last updated on 04/May/21

$$\mathrm{If}\cos \alpha +\cos \beta +\cos \gamma =0=\sin \alpha +\sin \beta +\sin \gamma ,\mathrm{then}$$$$\left(\mathrm{A}\right)\cos \left(2\alpha \right)+\cos \left(2\beta \right)+\cos \left(2\gamma \right)=0$$$$\left(\mathrm{B}\right)\sin \left(3\alpha \right)+\sin \left(3\beta \right)+\sin \left(3\gamma \right)=3\sin (\alpha +\beta +\gamma )$$$$\left(\mathrm{C}\right)\cos \left(3\alpha \right)+\cos \left(3\beta \right)+\cos \left(3\gamma \right)=3\cos (\alpha +\beta +\gamma )$$$$\left(\mathrm{D}\right)\sin \left(2\alpha \right)+\sin \left(2\beta \right)+\sin \left(2\gamma \right)=0$$

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