JEE Main 2024 Mathematics question
Not in JEE Main syllabus
The number of solutions of sin²x + (2 + 2x − x²)sin x − 3(x − 1)² = 0, where −π ≤ x ≤ π, is
Answer: 2
Solution
The equation factors as (sin x + 3)(sin x − (x − 1)²) = 0. Since sin x ≠ −3, sin x = (x − 1)², and this has 2 solutions in [−π, π].