2024 · Q54
Consider the following statements :
- 1In a triangle ABC, if sin A + sin B + sin C = 3√3/2, then the triangle can be equilateral.
- 2In 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 ?
Elementary MathematicsTrigonometry
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
sinA + sinB + sinC attains its maximum 3√3/2 exactly at A = B = C = 60°, so statement 1 is true. Likewise cosA + cosB + cosC attains its maximum 3/2 at A = B = C = 60°, so statement 2 is true. Both statements are correct: option (c).