Trigonometric Equations
Quadratic in cos θ — Counting Solutions in Interval
nta_pyq_2026_jan
Grade 11
Question:
Number of solutions of $\sqrt{3}\cos2\theta+8\cos\theta+3\sqrt{3}=0$, $\theta\in[-3\pi,2\pi]$ is:
Step-by-Step Solution
Key Concept: Use $\cos2\theta=2\cos^2\theta-1$: $2\sqrt{3}\cos^2\theta+8\cos\theta+2\sqrt{3}=0\Rightarrow\sqrt{3}\cos^2\theta+4\cos\theta+\sqrt{3}=0$. $\cos\theta=\dfrac{-4\pm2}{2\sqrt{3}}$.
5 solutions.
Correct Answer: 2