cos A + cos C = 4 sin² (B/2) then a,b,c are in a) A.P b) G.P c) H.P

Dear

cos A + cos C = 4 sin² (B/2)

2cos(A+C)/2 cos(A-C)/2  = 4 sin² (B/2)

cos(A-C)/2 =2 sin (B/2)

cos(A-C)/2   -sin (B/2)   =  sin (B/2)

cos(A-C)/2   -cos (A+C)/2  =  sin (B/2)

2sin(A/2)sin(C/2) =sin(B/2)

2√{(s-b)(s-c)/bc} √{(s-b)(s-a)/ba} =√{(s-a)(s-c)/ac}

2 (s-b)/b =1

2s =3b

a+c =2b

so a,b,c are in A.P

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