Consider the following statements :

1. In a triangle ABC, if sin A + sin B + sin C = 3√3/2, then the triangle can be equilateral.

2. In a triangle ABC, if cos A + cos B + cos C = 3/2, then the triangle can be equilateral.

Which of the statements given above is/are correct ?

Correct option is C

Solution:

Statement 1:

​$$\sin A + \sin B + \sin C = \frac{3 \sqrt{3}}{2}\\\sin A + \sin B + \sin C = \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2}\\It\ means \{ A = B = C = 60^\circ \}$$​​

The triangle can be equilateral.

Statement 2:

​$$\cos A + \cos B + \cos C = \frac{3}{2}\\\cos A + \cos B + \cos C = \frac{1}{2} + \frac{1}{2} + \frac{1}{2}$$

It means A = B = C = 60^∘ ​​

The triangle can be equilateral.

∴ The correct answer is Both 1 and 2.