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The number of solutions of the equation cos(πx−4−−−−−√)cos(πx√)=1cos(πx−4)cos(πx)=1 is A None B One C Two D More than two?
Most Upvoted Answer
The number of solutions of the equation cos(πx−4−−−−−√)cos(πx√)=1cos(π...
Solution:
Given equation:
cos(πx−4−−−−−√)cos(πx√) = cos(πx−4)cos(πx) = 1
Analysis:
To find the number of solutions of the given equation, we need to consider the properties of cosine function and the given equation.
Key Points:
- The cosine function has a period of 2π.
- The cosine function is periodic, meaning that the value of cos(x) is the same for x and x + 2π.
- The cosine function has a range of [-1, 1].
Explanation:
- Since the cosine function has a period of 2π, we can rewrite the given equation as:
cos(πx−4)cos(πx) = cos(2πx−4)cos(2πx) = 1
- Since the cosine function has a range of [-1, 1], the product of two cosine functions can only be 1 when both cosine functions are either 1 or -1.
- Therefore, the equation cos(2πx−4)cos(2πx) = 1 has at most two solutions, when both cosine functions are 1.
Conclusion:
The number of solutions of the given equation is C. Two.
This explanation provides a clear understanding of the properties of the cosine function and how they relate to the given equation.
Given equation:
cos(πx−4−−−−−√)cos(πx√) = cos(πx−4)cos(πx) = 1
Analysis:
To find the number of solutions of the given equation, we need to consider the properties of cosine function and the given equation.
Key Points:
- The cosine function has a period of 2π.
- The cosine function is periodic, meaning that the value of cos(x) is the same for x and x + 2π.
- The cosine function has a range of [-1, 1].
Explanation:
- Since the cosine function has a period of 2π, we can rewrite the given equation as:
cos(πx−4)cos(πx) = cos(2πx−4)cos(2πx) = 1
- Since the cosine function has a range of [-1, 1], the product of two cosine functions can only be 1 when both cosine functions are either 1 or -1.
- Therefore, the equation cos(2πx−4)cos(2πx) = 1 has at most two solutions, when both cosine functions are 1.
Conclusion:
The number of solutions of the given equation is C. Two.
This explanation provides a clear understanding of the properties of the cosine function and how they relate to the given equation.
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The number of solutions of the equation cos(πx−4−−−−−√)cos(πx√)=1cos(πx−4)cos(πx)=1 is A None B One C Two D More than two? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of solutions of the equation cos(πx−4−−−−−√)cos(πx√)=1cos(πx−4)cos(πx)=1 is A None B One C Two D More than two? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of solutions of the equation cos(πx−4−−−−−√)cos(πx√)=1cos(πx−4)cos(πx)=1 is A None B One C Two D More than two?.
The number of solutions of the equation cos(πx−4−−−−−√)cos(πx√)=1cos(πx−4)cos(πx)=1 is A None B One C Two D More than two? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of solutions of the equation cos(πx−4−−−−−√)cos(πx√)=1cos(πx−4)cos(πx)=1 is A None B One C Two D More than two? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of solutions of the equation cos(πx−4−−−−−√)cos(πx√)=1cos(πx−4)cos(πx)=1 is A None B One C Two D More than two?.
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