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iit jee Grade: 12
        

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

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

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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Badiuddin






 

7 years ago
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