A problem in Trigonometry (Properties of Triangles) v2

Question

Please help me with this sum:

In any triangle ABC, prove that $$a^2 b^2 c^2 \left (\sin {2A} +\sin {2B} + \sin {2C} \right) = 32 \Delta ^3$$

Here $\Delta $ means the area of the triangle.

My attempts:

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See https://math.stackexchange.com/questions/154505/prove-that-sin2a-sin2b-sin2c-4-sina-sinb-sinc-when-a-b-c-are and
(https://proofwiki.org/wiki/Area_of_Triangle_in_Terms_of_Circumradius or https://artofproblemsolving.com/community/c4h345932s1_prove_that_abc4r__abc) — lab bhattacharjee, May 12 '17 at 06:37
Have you noticed the answer, how it is linked with the links I've supplied — lab bhattacharjee, May 12 '17 at 07:15

score 0 · Accepted Answer · answered May 12 '17 at 07:14

0

Check that

So, $$LHS = 4(bc\sin A)(ca\sin B)(ab\sin C) = 32 \Delta^3.$$

answered May 12 '17 at 07:14

GAVD

1 Answers1