JEE Main 2024 Mathematics question
Not in JEE Main syllabus
The number of solutions of the equation 4 sin²x − 4 cos³x + 9 − 4 cos x = 0; x ∈ [−2π, 2π] is:
Answer: (B)
Solution
With c = cos x: 4c³ + 4c² + 4c − 13 = 0. The cubic is increasing and equals −1 at c = 1, so its only root exceeds 1: no solution.