JEE Main 2022 · 27 Jun · Shift 1 · Mathematics Q18

MathematicsSingle correct+4 / -1Question 18 of 90

The value of $\cos\left(\dfrac{2\pi}7\right)+\cos\left(\dfrac{4\pi}7\right)+\cos\left(\dfrac{6\pi}7\right)$ is equal to :

-1

-\dfrac12

-\dfrac13

-\dfrac14

Answer and worked solution

Official answer: B

Seventh roots of unity. The six non-real ones sum to $-1$ and pair up as $2\cos\frac{2k\pi}7$ , so $2(\text{sum})=-1$ .

Value $-\frac12$ .

(B)

Topics:Trigonometric ratios and identities Roots of unity

JEE Main 2022 · 27 Jun · Shift 1, Mathematics question 18