JEE Main 2026 Mathematics question

Not in JEE Main syllabus

Let S = {x ∈ [−π, π] : sin x(sin x + cos x) = a, a ∈ ℤ}. Then n(S) is equal to:

Answer: (D)

Solution

sin x(sin x + cos x) = ½ + (√2/2) sin(2x − π/4) has range [(1 − √2)/2, (1 + √2)/2] ≈ [−0.21, 1.21], so a = 0 or 1. a = 0: sin x = 0 (x

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Question ID VK-015196