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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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