JEE Exam > JEE Questions > Find the smallest positive integer p for whic...
Start Learning for Free
Find the smallest positive integer 'p' for which the equation cos (p sinx) = sin (p cosx) has a solution in [0, 2π].
Correct answer is '2'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Find the smallest positive integer p for which the equation cos (p sin...
Most Upvoted Answer
Find the smallest positive integer p for which the equation cos (p sin...
Approach:
To find the smallest positive integer p for which the given equation has a solution in the interval [0, 2π], we can analyze the properties of trigonometric functions.
Analysis:
- We know that the period of sin(x) is 2π and the period of cos(x) is also 2π.
- Let's consider the equation cos(psinx) = sin(pcosx) for a general value of p.
- Since the period of sin and cos is 2π, the equation will have a solution if the period of psinx is a multiple of 2π and the period of pcosx is also a multiple of 2π.
- This means that p must be an integer multiple of 2 for the equation to have a solution in the interval [0, 2π].
Solution:
- The smallest positive integer p for which the equation cos(psinx) = sin(pcosx) has a solution in [0, 2π] is when p = 2.
- When p = 2, the period of 2sinx is 2π (since 2 is a multiple of 2) and the period of 2cosx is also 2π.
- Therefore, the equation cos(2sinx) = sin(2cosx) will have a solution in the interval [0, 2π].
- Hence, the smallest positive integer p for which the equation has a solution in [0, 2π] is p = 2.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
Find the smallest positive integer p for which the equation cos (p sinx) = sin (p cosx) has a solutionin [0, 2π].Correct answer is '2'. Can you explain this answer?
Question Description
Find the smallest positive integer p for which the equation cos (p sinx) = sin (p cosx) has a solutionin [0, 2π].Correct answer is '2'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Find the smallest positive integer p for which the equation cos (p sinx) = sin (p cosx) has a solutionin [0, 2π].Correct answer is '2'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the smallest positive integer p for which the equation cos (p sinx) = sin (p cosx) has a solutionin [0, 2π].Correct answer is '2'. Can you explain this answer?.
Find the smallest positive integer p for which the equation cos (p sinx) = sin (p cosx) has a solutionin [0, 2π].Correct answer is '2'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Find the smallest positive integer p for which the equation cos (p sinx) = sin (p cosx) has a solutionin [0, 2π].Correct answer is '2'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the smallest positive integer p for which the equation cos (p sinx) = sin (p cosx) has a solutionin [0, 2π].Correct answer is '2'. Can you explain this answer?.
Solutions for Find the smallest positive integer p for which the equation cos (p sinx) = sin (p cosx) has a solutionin [0, 2π].Correct answer is '2'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Find the smallest positive integer p for which the equation cos (p sinx) = sin (p cosx) has a solutionin [0, 2π].Correct answer is '2'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Find the smallest positive integer p for which the equation cos (p sinx) = sin (p cosx) has a solutionin [0, 2π].Correct answer is '2'. Can you explain this answer?, a detailed solution for Find the smallest positive integer p for which the equation cos (p sinx) = sin (p cosx) has a solutionin [0, 2π].Correct answer is '2'. Can you explain this answer? has been provided alongside types of Find the smallest positive integer p for which the equation cos (p sinx) = sin (p cosx) has a solutionin [0, 2π].Correct answer is '2'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Find the smallest positive integer p for which the equation cos (p sinx) = sin (p cosx) has a solutionin [0, 2π].Correct answer is '2'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup