For non-negative integer n , let f(n)= _ k=0 ^ n ( k+1 n+2 ) ( k+2 n+2 ) _ k=0 ^ n ^ 2 (…
Mathematics · JEE Advanced · NTA Exams — Trigonometry
For non-negative integer 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–1x takes values in [0, π], which of the following options is/are correct?
\[f(n)=\frac{\sum_{k=0}^{n} \sin \left(\frac{k+1}{n+2} \pi\right) \sin \left(\frac{k+2}{n+2} \pi\right)}{\sum_{k=0}^{n} \sin ^{2}\left(\frac{k+1}{n+2} \pi\right)}\]
Assuming cos–1x takes values in [0, π], which of the following options is/are correct?
- If
- sin(7 cos–1 f(5)) = 0
Answer
(C) sin(7 cos –1 f (5)) = 0
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