In triangle ABC, `sinA sin B + sin B sin C + sin C sin A = 9//4 and a = 2`, then the value of `sqrt3 Delta`, where `Delta` is the area of triangle, is _______

In triangle ABC, `sinA sin B + sin B sin C + sin C sin A = 9//4 and a

1.	In triangle ABC, `sinA sin B + sin B sin C + sin C sin A = 9//4 and a = 2`, then the value of `sqrt3 Delta`, where `Delta` is the area of triangle, is _______
Answer» Correct Answer - 3 The given equation is `4 sin A sin B + 4 sin B sin C + 4 sin C sin A = 9` `rArr 2 cos (A -B) -2 cos (A +B) + 2 cos (B -C)` `- 2 cos (B +C) + 2 cos (C -A) -2 cos (C + A) = 9` or `2 [cos (A -B) + cos (B -C) + cos (C -A)]` `= 9 -2 (cos A + cos B + cos C)` `ge 9 -2 xx (3)/(2) = 6` or `cos (A -B) + cos (B -C) + cos (C -A) ge 3` But `cos (A -B) le1, cos (B -C) le 1, cos (C -A) le 1` or `cos (A -B) = 1, cos (B -C) =1, cos (C -A) = 1` Thus, `A = B = C`, i.e., triangle ABC is an equilateral triangle Hence, `Delta = sqrt3`

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In triangle ABC, `sinA sin B + sin B sin C + sin C sin A = 9//4 and a = 2`, then the value of `sqrt3 Delta`, where `Delta` is the area of triangle, is _______

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