Question

IN TRAINGLE ABC if A =3c then a-c/2c
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Answer 1

Answer:

sin B/2

Step-by-step explanation:

Given  

IN TRAINGLE ABC if A =3c then a-c/2c

We know that from sine rule we have

a = 2 R sin A

c = 2R sin C

So a – c / 2c = 2Rsin A – 2Rsin C / 2 x 2R sin C

                   = 2R(sin A – sin C) / 2 x 2R sin C

                  = sin A – sin C / 2sin C

               = 2 sin A – C / 2 cos A + C / 2 / 2 sin C / 2 cos C / 2

In triangle ABC  

            A + C / 2 = π / 2 – B / 2

Substituting we get

         =  2 sin A – C / 2 cos (π /2 – B / 2) / 2 sin C/2 cos C/2

           Now A = 3C

= 2 sin 3C – C / 2 sin B/2 / 2sin C

       = 2 Sin C sin B / 2 / 2 Sin C

       = sin B/2      

Answer 2

Answer:

nice solution thank you