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 sin 3 α+8 sin 3 β+27 sin 3 γ is equal to

Question

MARKS Content Team · Accepted Answer

Correct answer: (B) 0. Let a=cos α+i sin α b=cos β+i sin β and c=cos γ+i sin γ Then, a+2 b+3 c=(cos α+2 cos β+3 cos γ) +i(sin α+2 sin β+3 sin γ)=0 ⇒ a^3+8 b^3+27 c^3=18 a b c (∵ . if .x+y+z=0 ⇒ x^3+y^3+z^3=3 x y z ) ⇒ cos 3 α+8 cos 3 β+27 cos 3 γ and sin 3 α+8 sin 3 β+27 sin 3 γ =18 sin (α+β+γ) =18 sin π=0

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 $\sin 3 \alpha+8 \sin 3 \beta+27 \sin 3 \gamma$ is equal to

Solution

Relevant Questions