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Let, α and β be real. Find the set of all values of β for which the system of equation βx + sin α*y + cosα*z = 0, x + cosα * y + sinα * z = 0 , -x + sinα*y – cosα * z = 0 has a non-trivial solution. For β = 1 what are all values of α?
  • a)
    2α = 2nπ ± π/2 + π/2
  • b)
    2α = 2nπ ± π/2 + π/4
  • c)
    2α = 2nπ ± π/4 + π/4
  • d)
    2α = 2nπ ± π/4 + π/2
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Let, α and β be real. Find the set of all values of β ...
The given system have non-trivial solution if 
On opening the determinant we get β = sin 2α + cos 2 α
Therefore, -√2 ≤ β ≤ √2
Now, for β = 1,
sin 2α + cos 2 α = 1
⇒(1/√2)sin 2α + (1/√2) cos 2α = (1/√2)
Or, cos(2α – π/4) = 1/√2 = cos(2nπ ± π/4)
⇒ 2α = 2nπ ± π/4 + π/4
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Let, α and β be real. Find the set of all values of β for which the system of equation βx + sin α*y + cosα*z = 0, x + cosα * y + sinα * z = 0 , -x + sinα*y – cosα * z = 0 has a non-trivial solution. For β = 1 what are all values of α?a)2α = 2nπ ± π/2 + π/2b)2α = 2nπ ± π/2 + π/4c)2α = 2nπ ± π/4 + π/4d)2α = 2nπ ± π/4 + π/2Correct answer is option 'C'. Can you explain this answer?
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Let, α and β be real. Find the set of all values of β for which the system of equation βx + sin α*y + cosα*z = 0, x + cosα * y + sinα * z = 0 , -x + sinα*y – cosα * z = 0 has a non-trivial solution. For β = 1 what are all values of α?a)2α = 2nπ ± π/2 + π/2b)2α = 2nπ ± π/2 + π/4c)2α = 2nπ ± π/4 + π/4d)2α = 2nπ ± π/4 + π/2Correct answer is option 'C'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Let, α and β be real. Find the set of all values of β for which the system of equation βx + sin α*y + cosα*z = 0, x + cosα * y + sinα * z = 0 , -x + sinα*y – cosα * z = 0 has a non-trivial solution. For β = 1 what are all values of α?a)2α = 2nπ ± π/2 + π/2b)2α = 2nπ ± π/2 + π/4c)2α = 2nπ ± π/4 + π/4d)2α = 2nπ ± π/4 + π/2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let, α and β be real. Find the set of all values of β for which the system of equation βx + sin α*y + cosα*z = 0, x + cosα * y + sinα * z = 0 , -x + sinα*y – cosα * z = 0 has a non-trivial solution. For β = 1 what are all values of α?a)2α = 2nπ ± π/2 + π/2b)2α = 2nπ ± π/2 + π/4c)2α = 2nπ ± π/4 + π/4d)2α = 2nπ ± π/4 + π/2Correct answer is option 'C'. Can you explain this answer?.
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