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What will be the nature of the equation sin(x + α)/sin(x + β)?
- a)Possess only minimum value
- b)Possess only maximum value
- c)Does not possess a maximum or minimum value
- d)Data inadequate
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
What will be the nature of the equation sin(x + α)/sin(x + &beta...
Nature of the equation sin(x + α)/sin(x + β):
Sin(x + α)/sin(x + β) is a trigonometric expression involving the sine function. The nature of this expression depends on the values of α and β.
- Does not possess a maximum or minimum value:
When we simplify the given expression sin(x + α)/sin(x + β), we get a trigonometric expression that does not have a maximum or minimum value. This is because the sine function oscillates between -1 and 1 for all values of x. The ratio of two sine functions will also oscillate between certain values without reaching a maximum or minimum point.
- Data inadequate:
Without knowing the specific values of α and β, we cannot determine if the expression possesses only a minimum value, only a maximum value, or neither. The nature of the expression sin(x + α)/sin(x + β) is dependent on the values of α and β, so without this information, we cannot definitively say whether it has a maximum or minimum value.
Therefore, the correct nature of the equation sin(x + α)/sin(x + β) is that it does not possess a maximum or minimum value.
Sin(x + α)/sin(x + β) is a trigonometric expression involving the sine function. The nature of this expression depends on the values of α and β.
- Does not possess a maximum or minimum value:
When we simplify the given expression sin(x + α)/sin(x + β), we get a trigonometric expression that does not have a maximum or minimum value. This is because the sine function oscillates between -1 and 1 for all values of x. The ratio of two sine functions will also oscillate between certain values without reaching a maximum or minimum point.
- Data inadequate:
Without knowing the specific values of α and β, we cannot determine if the expression possesses only a minimum value, only a maximum value, or neither. The nature of the expression sin(x + α)/sin(x + β) is dependent on the values of α and β, so without this information, we cannot definitively say whether it has a maximum or minimum value.
Therefore, the correct nature of the equation sin(x + α)/sin(x + β) is that it does not possess a maximum or minimum value.
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Community Answer
What will be the nature of the equation sin(x + α)/sin(x + &beta...
Let, y = sin(x + α)/sin(x + β)
Then,
dy/dx = [cos(x + α)sin(x + β) – sin(x + α)cos(x + β)]/sin2(x + β)
= sin(x+β – x-α)/sin2(x + β)
Or sin(β – α)/sin2(x + β)
So, for minimum or maximum value of x we have,
dy/dx = 0
Or sin(β – α)/sin2(x + β) = 0
Or sin(β – α) = 0 ……….(1)
Clearly, equation (1) is independent of x; hence, we cannot have a real value of x as root of equation (1).
Therefore, y has neither a maximum or minimum value.
Then,
dy/dx = [cos(x + α)sin(x + β) – sin(x + α)cos(x + β)]/sin2(x + β)
= sin(x+β – x-α)/sin2(x + β)
Or sin(β – α)/sin2(x + β)
So, for minimum or maximum value of x we have,
dy/dx = 0
Or sin(β – α)/sin2(x + β) = 0
Or sin(β – α) = 0 ……….(1)
Clearly, equation (1) is independent of x; hence, we cannot have a real value of x as root of equation (1).
Therefore, y has neither a maximum or minimum value.
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What will be the nature of the equation sin(x + α)/sin(x + β)?a)Possess only minimum valueb)Possess only maximum valuec)Does not possess a maximum or minimum valued)Data inadequateCorrect answer is option 'C'. Can you explain this answer?
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What will be the nature of the equation sin(x + α)/sin(x + β)?a)Possess only minimum valueb)Possess only maximum valuec)Does not possess a maximum or minimum valued)Data inadequateCorrect 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 What will be the nature of the equation sin(x + α)/sin(x + β)?a)Possess only minimum valueb)Possess only maximum valuec)Does not possess a maximum or minimum valued)Data inadequateCorrect 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 What will be the nature of the equation sin(x + α)/sin(x + β)?a)Possess only minimum valueb)Possess only maximum valuec)Does not possess a maximum or minimum valued)Data inadequateCorrect answer is option 'C'. Can you explain this answer?.
What will be the nature of the equation sin(x + α)/sin(x + β)?a)Possess only minimum valueb)Possess only maximum valuec)Does not possess a maximum or minimum valued)Data inadequateCorrect 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 What will be the nature of the equation sin(x + α)/sin(x + β)?a)Possess only minimum valueb)Possess only maximum valuec)Does not possess a maximum or minimum valued)Data inadequateCorrect 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 What will be the nature of the equation sin(x + α)/sin(x + β)?a)Possess only minimum valueb)Possess only maximum valuec)Does not possess a maximum or minimum valued)Data inadequateCorrect answer is option 'C'. Can you explain this answer?.
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