For non-negative integer n, let f(n) (su...

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`

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1,2,4

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