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Question

If sin(2αβγ)+8sin(2βγα)+27sin(2γαβ)=P and sin(α+β)+sin(β+γ)+sin(γ+α)=Q then P+Q is equal to

A
36
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B
18
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C
9
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D
0
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Solution

The correct option is D 0
Let α+β+γ=0 .....(1)
P=sin(2αβγ)+8sin(2βγα)+27sin(2γαβ)
=sin3α+8sin3β+27sin3γ =3(1)(2)(3)sin(α+β+γ)=0 ....using (1) and
Q=sin(α+β)+sin(β+γ)+sin(γ+α)=(sinα+sinβ+sinγ)=0
P+Q=0

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