JEE Main 2026 · 6 Apr · Shift 1 · Mathematics Q14

MathematicsSingle correct+4 / -1Question 14 of 75

Let $S=\left\{\theta\in(-2\pi,2\pi):\cos\theta+1=\sqrt3\sin\theta\right\}$ . Then $\displaystyle\sum_{\theta\in S}\theta$ is equal to:

-\dfrac{2\pi}3

-\dfrac{4\pi}3

\dfrac{2\pi}3

\dfrac{4\pi}3

Answer and worked solution

Official answer: B

Rewrite. $\sqrt3\sin\theta-\cos\theta=1$ becomes $\sin\left(\theta-\tfrac\pi6\right)=\tfrac12$ .

Solutions. $\theta=\tfrac\pi3+2n\pi$ or $\theta=\pi+2n\pi$ . In $(-2\pi,2\pi)$ :
$\theta=\frac\pi3,\ -\frac{5\pi}3,\ \pi,\ -\pi.$

Sum: $-\dfrac{4\pi}3$ .

(B)

Topics:Trigonometric equations

JEE Main 2026 · 6 Apr · Shift 1, Mathematics question 14