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  4. If cos α+2 cos β+3 cos γ=0, sin α+2 sin β+3 sin γ=0 and α+β+γ=π, then 3α+8 sin 3β+27 sin 3 γ=

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Q. If $cos\,\alpha+2\,cos\,\beta+3\,cos\,\gamma=0, sin\,\alpha+2\,sin\,\beta+3\,sin\,\gamma=0$ and $\alpha+\beta+\gamma=\pi$, then $3\alpha+8\,sin\,3\beta+27\,sin\,3\,\gamma$=

Trigonometric Functions

Solution:

$sin\,3\alpha+8\,sin\,3 \beta+27\,sin\,3\gamma=18\,sin (\alpha+\beta+\gamma)$
$=18\,sin\,\pi=0$