JEE (Advanced) 2019 Paper-2 Question 39

Question 39

For non-negative integers n,let
$$f(n) = \frac{{\sum_{k = 0}^n}\sin \left(\frac{k + 1}{n + 2}\pi\right) \sin \left(\frac{k + 2}{n + 2}\pi\right)}{\sum_{k = 0}^n \sin^2 \left(\frac{k + 1}{n + 2}\pi\right)} $$
Assuming $$\cos^{-1}x$$ takes values in $$[0,\pi],$$ which of the following options is/are correct?

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