Question

For non-negative integer n, let f(n) `(sum_(k=0)^(n)sin((k+1)/(k+2)pi)sin((k+2)/(n+2)pi))/(sum_(k=0)^(n)sin^(2)((k+1)/(n+2)pi))`
Assuming `cos^(-1)x` takes values in `[0,pi]`, which of the following options is/are correct?
A. `sin(7cos^(-1)f(5))=0`
B. `f(4)=sqrt(3)/2`
C. `underset(ntoinfty)"lim"f(n)=1/2`
D. If `alpha=tan(cos^(-1)f(6))`, then `alpha^(2)+2alpha-1=0`

Answer 1

Correct Answer - 1,2,4