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Question

If x+y+z=π and
Δ=∣ ∣sin3xsin3ysin3zsinxsinysinzcosxcosycosz∣ ∣
then Δ equals

A
3
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B
1
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C
0
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D
4
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Solution

The correct option is A 0
Δ=∣ ∣sin3xsin3ysin3zsinxsinysinzcosxcosycosz∣ ∣

=∣ ∣ ∣3sinx4sin3x3siny4sin3y3sinz4sin3zsinxsinysinzcosxcosycosz∣ ∣ ∣

=∣ ∣3sinx3siny3sinzsinxsinysinzcosxcosycosz∣ ∣∣ ∣ ∣4sin3x4sin3y4sin3z000000∣ ∣ ∣

=3sinx(sinycoszsinzcosy)3siny(sinxcoszsinzcosx)+3sinz(sinxcosysinycosx)0

=0

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