For non – negative integers n, let f(n)= {\sum_{k=0}^{n}\sin( \frac{k+1}{n+2}\pi)\sin( \frac{k+2}{n+2}\pi)}/{\sum_{k=0}^{n}\sin^{2}( \frac{k+1}{n+2}\pi)}Assuming \cos^{-1}x takes values in [0,\pi] which of the following options is/are correct? [JEE Adv 2019 P2]

If \alpha=\tan(\cos^{-1}f(6)),\text{then}\alpha^{2}+2\alpha-1=0

\lim_{n\to\infty}f(n)= \frac{1}{2}

Trigonometric Functions & Equations

Section: Mathematics

Question : 9 of 30

Marks: +1, -0

For non – negative integers n, let

f(n)=‌‌

∑

k=0

sin(‌‌

k+1

n+2

π)‌sin(‌‌

k+2

n+2

π)

∑

k=0

sin2(‌‌

k+1

n+2

π)

Assuming cos−1x takes values in [0,π] which of the following options is/are correct?

[JEE Adv 2019 P2]

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