Home/
Competitive Exams/
JEE Main & Advanced/
Mathematics/
Trigonometry/
Question 200043
JEE Mathematics · Hard

Trigonometry: Sum of series MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

Timer-based practiceDetailed answer reviewMobile-friendly flow
Sum of seriesHardQuestion 200043

Question

The value of cos 2π/7 + cos 4π/7 + cos 6π/7 is:
  1. A
    1/2
  2. B
    −1/2
    Correct
  3. C
    0
  4. D
    1

Correct answer

−1/2

Explanation

The sum of cosines of angles in arithmetic progression: sum = (1/2)(sin(nα/2)/sin(α/2)) cos(first + last)/2. For 7th roots of unity: cos(2π/7) + cos(4π/7) + ... + cos(12π/7) = −1. Taking the real parts symmetrically: cos(2π/7) + cos(4π/7) + cos(6π/7) = −1/2.

Review Trigonometry notesStart timed chapter practice