JEE Advanced 2018 Paper 2 Mathematics Q6

Mathematics

Problem

Let f : (0, π) → ℝ be a twice differentiable function such that limₜ→ₓ[(f(x) sin t − f(t) sin x)/(t − x)] = sin²x for all x ∈ (0, π). If f(π/6) = −π/12, then which of the following statement(s) is (are) TRUE?

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