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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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