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In a triangle ABC a^2b^2c^2(sin 2A + sin 2B + sin 2C) =

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In a triangle ABC a2b2c2(sin 2A + sin 2B + sin 2C) =

(A)  Δ3

(B)  8Δ3

(C)  16 Δ3

(D)  32 Δ3

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Correct option (D)  32Δ3

a2b2c2 (sin 2A + sin 2B + sin 2C)

= a2b2c2 (2sin (A + B) cos (A – B) + 2 sin C cos C)

= a2b2c2 2 sin C [cos (A – B) – cos (A + B)]

= a2b2c2 [4sin A sin B sin C]

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