when i simplify this equation i can't understand the sin(n+1)A,sin(n-1)A.
Numerator
-------------
N = sin(n+1)A - sin(n-1)A
= 2cos[{(n+1)A+(n-1)A}/2]sin[{(n+1)A-(n-1)A}/2]
= 2cos(2nA/2)sin(2A/2)
= 2cos(nA)sin(A)
Denominator
-------------
D = cos(n+1)A+2cos(nA)+cos(n-1)A
= 2cos(nA)+cos(n+1)A+cos(n-1)A
= 2cos(nA)+2cos[{(n+1)A+(n-1)A}/2]cos[{(n+1)A-(n-1)A}/2]
= 2cos(nA)+2cos(nA)cosA
So D=2cos(nA)(1+cosA)
So,
N/D
=2cos(nA)sin(A)/2cos(nA)(1+cosA)
= sinA/(1+cosA)
= 2sin(A/2)cos(A/2)/2cos^{2}(A/2)
=sin(A/2)/cos(A/2)
=tan(A/2)