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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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