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If x sinθ=y sin(θ+2 Π/3)=z sin(θ+4 Π/3) then prove that Σxy=0. Please explain with full steps.

If x sinθ=y sin(θ+2 Π/3)=z sin(θ+4 Π/3) then prove that Σxy=0.
Please explain with full steps.

Grade:11

1 Answers

Akshay
185 Points
8 years ago
use sin(a+b) = sin a * cos b + cos a * sin b,
1: x sinθ, 2: ysin(θ+2pi/3), 3: zsin(θ+4pi/3)
equate 1 and 2, u will get tanθ = root(3)*y/(2x+y),
equate 1 and 3, u will get tanθ = -root(3)*z/(2x+z),
equating both tanθ obtained and simplying will help you get the result
 

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