JEE Advanced 2019 Paper 2 Mathematics Q3

Mathematics

Problem

For non-negative integers n, let f(n) = [Σₖ₌₀ⁿ sin((k + 1)π/(n + 2)) sin((k + 2)π/(n + 2))]/[Σₖ₌₀ⁿ sin²((k + 1)π/(n + 2))]. Assuming cos⁻¹x takes values in [0, π], which of the following options is/are correct?

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