Let A and B denote the statements: A: α + β + γ = 0 B: α + β + γ = 0 If (β-γ) + (γ-α) + (α-β) = -3/2 , then: - Mathematics MCQ AIEEE 2009 2026 | ExamTest.live

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Let A and B denote the statements: A : cos α + cos β + cos γ = 0 B : sin α + sin β + sin γ = 0 If cos (β - γ) + cos (γ - α) + cos (α - β) = - \frac{3}{2}, then:

Solution & Step-by-step Explanation

Given 2 [cos (β - γ) + cos (γ - α) + cos (α - β)] + 3 = 0 .We know (cos α + cos β + cos γ)^{2} + (sin α + sin β + sin γ)^{2} = (cos^{2} α + sin^{2} α) + (cos^{2} β + sin^{2} β) + (cos^{2} γ + sin^{2} γ) + 2 [cos α cos β + sin α sin β + \dots] = 1 + 1 + 1 + 2 [cos (α - β) + cos (β - γ) + cos (γ - α)] = 3 + 2 (- \frac{3}{2}) = 0 .Since the sum of squares of two real numbers is zero, each number must be zero. ⟹ cos α + cos β + cos γ = 0 and sin α + sin β + sin γ = 0 .

Try it yourself before checking the explanation above.

Let A and B denote the statements: A : cos α + cos β + cos γ = 0 B : sin α + sin β + sin γ = 0 If cos (β - γ) + cos (γ - α) + cos (α - β) = - \frac{3}{2}, then:

A is true and B is false

A is false and B is true

both A and B are true

both A and B are false

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