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JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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If cos⁡α+2cos⁡β+3cos⁡γ=sin⁡α+2sin⁡β+3sin⁡γ=0,\cos \alpha + 2\cos \mathrm{\beta } + 3\cos \mathrm{\gamma } = \sin \alpha + 2\sin \mathrm{\beta } + 3\sin \mathrm{\gamma } = 0, then the value of sin⁡3  α+8sin⁡3  β+27sin⁡3  γ\sin 3\;\alpha + 8\sin 3\;\mathrm{\beta } + 27\sin 3\;\mathrm{\gamma } is
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Correct option: C
18sin⁡(α+β+γ)18\sin \left( {\alpha + \beta + \gamma } \right)
Option C (18sin⁡(α+β+γ)18\sin \left( {\alpha + \beta + \gamma } \right)) is correct because it is derived from complex number manipulation and trigonometric identities given the initial conditions.

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