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📐 Mathematics  ·  Trigonometric Functions  ·  JEE

Sum of cosines: cosθ + cos(θ+2π/n) + cos(θ+4π/n) + ... (n terms) =

Answer: 0.

  • A n cosθ
  • B 0
  • C cosθ
  • D 1

Correct answer: B. 0

Explanation: Phasor method: each term is Re(e^(i(θ+2πk/n))). Sum = Re(e<sup>iθ</sup>·Σe<sup>2πik/n</sup>) for k=0..n−1. The inner sum is the sum of all n-th roots of unity = 0. Therefore total sum = 0 for all θ.

xy0 deg30 deg45 deg (1/sqrt2, 1/sqrt2)60 deg90 degcos45sin45

Unit circle with standard angles 0, 30, 45, 60, 90 degrees; at 45 degrees the point is (cos45, sin45) = (1/sqrt2, 1/sqrt2).

Concept context

Ratios, identities, and applications in triangles

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