SOLUTION: Let a, b, c be three sides opposite to the angles A, B, C respectively in a triangle ABC. Find 2ac.Sin(A + C

SOLUTION: Let a, b, c be three sides opposite to the angles A, B, C respectively in a triangle ABC. Find 2ac.Sin(A + C - B)/2?

Question 1184170: Let a, b, c be three sides opposite to the angles A, B, C respectively in a triangle ABC. Find 2ac.Sin(A + C - B)/2?
Answer by ikleyn(52859) (Show Source): You can put this solution on YOUR website!
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Let a, b, c be three sides opposite to the angles A, B, C respectively in a triangle ABC.
Find 2ac.Sin((A + C - B)/2).
~~~~~~~~~~~~~~~~~~~~~~~~

First,   =  =  = .

THEREFORE,   =  = cos(B).



Next, due to the cosine law for triangle ABC

     =  +  - .



It implies

    2ac*cos(B) = a^2 + c^2 - b^2



Now we can write the final identity

     = 2ac*cos(B) = .



ANSWER.   = .

Solved.

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