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?
A.1 only
B.2 only
C.Both 1 and 2✓ Correct
D.Neither 1 nor 2
Explanation
For an equilateral triangle, A = B = C = 60°. Then sin A + sin B + sin C = 3 sin 60° = 3 × (√3/2) = 3√3/2. ✓. And cos A + cos B + cos C = 3 cos 60° = 3 × (1/2) = 3/2. ✓. Both statements are correct.
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