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The system of equations : 
2x cosθ + y sin 2θ – 2 sin θ = 0
x sin 2θ + 2y sin2 θ = –2cos θ
x sin θ – y cos θ = 0 , for all values of θ, can
  • a)
    have a unique non - trivial solution
  • b)
    not have a solution
  • c)
    have infinite solutions
  • d)
    have a trivial solution
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The system of equations :2x cos2θ + y sin 2θ – 2 sin...
slope of (1) and (2) is cot θ ⇒ (1) and (2) are parallel and slope of (3) is tanθ ⇒ no solution.
Using R2 → R2 – (2 cosθ) R3 and R1 → R1 + (2 sinθ)R3 , the value of determinat is 4]
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Most Upvoted Answer
The system of equations :2x cos2θ + y sin 2θ – 2 sin...

Explanation:

Given System of Equations:

The given system of equations is:
1. \(2x \cos2\theta + y \sin 2\theta - 2 \sin \theta = 0\)
2. \(x \sin 2\theta + 2y \sin2 \theta = -2 \cos \theta\)
3. \(x \sin \theta - y \cos \theta = 0\)

Explanation of Option 'B' (Not have a solution):

- To determine if the system has a solution, we can use the concept of determinant of coefficients.
- If the determinant of coefficients is zero, the system may have no solution or infinite solutions, but not a unique solution.
- The determinant of coefficients for this system of equations is zero.
- Therefore, the given system of equations does not have a unique non-trivial solution.
- Since the determinant is zero, the system is inconsistent and does not have a solution.

Conclusion:

The correct answer is option 'B' - "Not have a solution".
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The system of equations :2x cos2θ + y sin 2θ – 2 sin θ = 0x sin 2θ + 2y sin2 θ = –2cos θx sin θ – y cos θ = 0 , for all values of θ, cana)have a unique non - trivial solutionb)not have a solutionc)have infinite solutionsd)have a trivial solutionCorrect answer is option 'B'. Can you explain this answer?
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The system of equations :2x cos2θ + y sin 2θ – 2 sin θ = 0x sin 2θ + 2y sin2 θ = –2cos θx sin θ – y cos θ = 0 , for all values of θ, cana)have a unique non - trivial solutionb)not have a solutionc)have infinite solutionsd)have a trivial solutionCorrect 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 The system of equations :2x cos2θ + y sin 2θ – 2 sin θ = 0x sin 2θ + 2y sin2 θ = –2cos θx sin θ – y cos θ = 0 , for all values of θ, cana)have a unique non - trivial solutionb)not have a solutionc)have infinite solutionsd)have a trivial solutionCorrect 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 The system of equations :2x cos2θ + y sin 2θ – 2 sin θ = 0x sin 2θ + 2y sin2 θ = –2cos θx sin θ – y cos θ = 0 , for all values of θ, cana)have a unique non - trivial solutionb)not have a solutionc)have infinite solutionsd)have a trivial solutionCorrect answer is option 'B'. Can you explain this answer?.
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