Consider the following statements:<br>1. In a triangle ABC, if \sin A+\sin B+\sin C=\frac{3\sqrt{3}}{2} then the triangle can be equilateral.<br>2. In a triangle ABC, if \cos A+\cos B+\cos C=\frac{3}{2} then the triangle can be equilateral.<br>Which of the statements given above is/are correct?

Explanation

Test the condition for an equilateral triangle, where all angles A = B = C = 60^{\circ}. For Statement 1: 3 \times \sin(60^{\circ}) = 3 \times \frac{\sqrt{3}}{2} = \frac{3\sqrt{3}}{2}, which matches. For Statement 2: 3 \times \cos(60^{\circ}) = 3 \times \frac{1}{2} = \frac{3}{2}, which also matches. Therefore, both conditions hold true for an equilateral triangle.

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