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Question
If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`. find the value of xy + yz + zx
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Solution
Let x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)` = k (say)
`"k"/x` = cos θ
`"k"/y = cos (theta + (2pi)/3)`
`"k"/z = cos (theta + (4pi)/3)`
`"k"/x + "k"/y + "k"/z = cos theta + cos(theta + (2pi)/3) + cos(theta + (4pi)/3)`
`"k"/x + "k"/y + "k"/z` = 0
`"k"[(yz + xz + xy)/(xyz)]` = 0
⇒ xy + yz + zx = 0
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