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If x cos θ = ycos(θ+2π3)=zcos(θ+4π3). find the value of xy + yz + zx

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प्रश्न

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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उत्तर

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

shaalaa.com
Trigonometric Functions and Their Properties
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Trigonometry - Exercise 3.4 [पृष्ठ १०९]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 3 Trigonometry
Exercise 3.4 | Q 16 | पृष्ठ १०९

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