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Let A and B denote the statements A : cosα + cosβ + cosγ = 0 B : sinα + sinβ + sinγ = 0
If cos (β – γ) + cos (γ – α) + cos (α – β) =       then : [2009]
  • a)
    A is false and B is true
  • b)
    both A and B are true
  • c)
    both A and B are false
  • d)
    A is true and B is false
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Let A and B denote the statements A : cosα + cosβ + cos&gam...
We have
cos (β – γ) + cos (γ – α) + cos (α – β) =
⇒ 2 [cos (β – γ) + cos (γ – α) + cos (α – β)] + 3 = 0
⇒ 2 [cos (β – γ) + cos (γ – α) + cos (α – β)]
+ sin2α + cos2α + sin2β + cos2β + sin2γ + cos2γ = 0
⇒ [sin2α + sin2β + sin2γ + 2 sinα  sinβ + 2 sinβ sinγ
+ 2 sinγ sinα ] + [cos2α + cos2β + cos2γ + 2cosα cosβ
+ 2 cosβ cosγ + 2cosγ cosα] = 0
⇒ [sinα + sinβ + sinγ]2 + (cos2α + cosβ + cos2γ )2= 0
⇒ sinα + sinβ + sinγ = 0 and cosα + cosβ + cosγ =0
∴ A and B both are true.
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Let A and B denote the statements A : cosα + cosβ + cosγ = 0 B : sinα + sinβ + sinγ = 0If cos (β – γ) + cos (γ – α) + cos (α – β) = then : [2009]a)A is false and B is trueb)both A and B are truec)both A and B are falsed)A is true and B is falseCorrect answer is option 'B'. Can you explain this answer?
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Let A and B denote the statements A : cosα + cosβ + cosγ = 0 B : sinα + sinβ + sinγ = 0If cos (β – γ) + cos (γ – α) + cos (α – β) = then : [2009]a)A is false and B is trueb)both A and B are truec)both A and B are falsed)A is true and B is falseCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let A and B denote the statements A : cosα + cosβ + cosγ = 0 B : sinα + sinβ + sinγ = 0If cos (β – γ) + cos (γ – α) + cos (α – β) = then : [2009]a)A is false and B is trueb)both A and B are truec)both A and B are falsed)A is true and B is falseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let A and B denote the statements A : cosα + cosβ + cosγ = 0 B : sinα + sinβ + sinγ = 0If cos (β – γ) + cos (γ – α) + cos (α – β) = then : [2009]a)A is false and B is trueb)both A and B are truec)both A and B are falsed)A is true and B is falseCorrect answer is option 'B'. Can you explain this answer?.
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