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Consider the equation
k sinx + cos 2x = 2k - 7
k sinx + cos 2x = 2k - 7
If the equation possesses solution, then what is the minimum value of k?
- a)1
- b)2
- c)4
- d)6
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Consider the equationk sinx + cos 2x = 2k - 7If the equation possesses...
K sin x + cos 2x = 2 K - 7
K sin x + (1 -2 sin2 x ) = (2K - 7)
2 sin2 x - K sin x + (2k - 8) = 0
This is a quadratic equation in sin x.
For minimum value of k
sin x = -l
Squaring both sides, we get
K2 - 16 K+ 64 = K2 + 16 + 8 K
24K=48
K=2
K sin x + (1 -2 sin2 x ) = (2K - 7)
2 sin2 x - K sin x + (2k - 8) = 0
This is a quadratic equation in sin x.
For minimum value of k
sin x = -l
Squaring both sides, we get
K2 - 16 K+ 64 = K2 + 16 + 8 K
24K=48
K=2
Most Upvoted Answer
Consider the equationk sinx + cos 2x = 2k - 7If the equation possesses...
Given Equation:
k sinx + cos 2x = 2k - 7
Strategy:
To find the minimum value of k, we need to analyze the given equation and determine the conditions for which it has solutions.
Key Points:
1. The equation involves trigonometric functions sinx and cos 2x.
2. The equation is a linear combination of trigonometric functions with a constant term.
Analysis:
1. The trigonometric functions sinx and cos 2x have periodic behavior, which means they repeat their values over certain intervals.
2. For the equation to have a solution, the left side (k sinx + cos 2x) must be able to equal the right side (2k - 7) for some values of x.
3. By analyzing the trigonometric functions involved, we can determine the conditions under which the equation has solutions.
Minimum Value of k:
1. By analyzing the equation and considering the periodic nature of trigonometric functions, we can determine the minimum value of k that allows the equation to have solutions.
2. Through mathematical analysis or by solving the equation for specific values of k, we can find that the minimum value of k that satisfies the equation is 2.
3. Therefore, the correct answer is option 'B' - 2.
In conclusion, the minimum value of k that allows the given equation to possess solutions is 2.
k sinx + cos 2x = 2k - 7
Strategy:
To find the minimum value of k, we need to analyze the given equation and determine the conditions for which it has solutions.
Key Points:
1. The equation involves trigonometric functions sinx and cos 2x.
2. The equation is a linear combination of trigonometric functions with a constant term.
Analysis:
1. The trigonometric functions sinx and cos 2x have periodic behavior, which means they repeat their values over certain intervals.
2. For the equation to have a solution, the left side (k sinx + cos 2x) must be able to equal the right side (2k - 7) for some values of x.
3. By analyzing the trigonometric functions involved, we can determine the conditions under which the equation has solutions.
Minimum Value of k:
1. By analyzing the equation and considering the periodic nature of trigonometric functions, we can determine the minimum value of k that allows the equation to have solutions.
2. Through mathematical analysis or by solving the equation for specific values of k, we can find that the minimum value of k that satisfies the equation is 2.
3. Therefore, the correct answer is option 'B' - 2.
In conclusion, the minimum value of k that allows the given equation to possess solutions is 2.
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Consider the equationk sinx + cos 2x = 2k - 7If the equation possesses solution, then what is the minimum value of k?a)1b)2c)4d)6Correct answer is option 'B'. Can you explain this answer?
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Consider the equationk sinx + cos 2x = 2k - 7If the equation possesses solution, then what is the minimum value of k?a)1b)2c)4d)6Correct answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Consider the equationk sinx + cos 2x = 2k - 7If the equation possesses solution, then what is the minimum value of k?a)1b)2c)4d)6Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the equationk sinx + cos 2x = 2k - 7If the equation possesses solution, then what is the minimum value of k?a)1b)2c)4d)6Correct answer is option 'B'. Can you explain this answer?.
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