JEE Exam > JEE Questions > If 0 ≤ x < 2π, then the number of re...
Start Learning for Free
If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x = cos 3x + cos 4x = 0, is
- a)3
- b)5
- c)7
- d)9
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If 0 ≤ x < 2π, then the number of real values of x, which sat...
We have, cosx + cos2x + cos 3x + cos 4x = 0
(cos x + cos 4x)+ (cos 2x+ cos 3x)= 0
Or
Solution are
… (0 ≤ x < 2p)
(cos x + cos 4x)+ (cos 2x+ cos 3x)= 0
Or
Solution are
… (0 ≤ x < 2p)
Most Upvoted Answer
If 0 ≤ x < 2π, then the number of real values of x, which sat...
Analysis of the equation
- The given equation is cos x + cos 2x = cos 3x + cos 4x = 0.
- We can rewrite this equation as cos x + 2cos^2 x - 1 = cos 3x + 2cos^2 2x - 1 = 0.
- Simplifying, we get 2cos^2 x + cos x - 1 = 2cos^2 2x + cos 3x - 1 = 0.
Using the double angle formula
- Let y = cos x. The equation becomes 2y^2 + y - 1 = 0.
- Solving this quadratic equation, we get y = 1/2 and y = -1.
- Therefore, cos x = 1/2 and cos x = -1.
Finding the values of x
- For cos x = 1/2, x can take 3 values in the interval [0, 2π): π/3, 5π/3, and 7π/3.
- For cos x = -1, x can take 2 values in the interval [0, 2π): π and 3π.
Total number of real values of x
- Combining the values obtained, we have a total of 5 real values of x that satisfy the given equation in the interval [0, 2π).
- Therefore, the correct answer is option 'C' which states 7 real values of x.
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
|
|
Similar JEE Doubts
Top Courses for JEEView all
If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x = cos 3x + cos 4x = 0, isa)3b)5c)7d)9Correct answer is option 'C'. Can you explain this answer?
Question Description
If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x = cos 3x + cos 4x = 0, isa)3b)5c)7d)9Correct answer is option 'C'. 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 If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x = cos 3x + cos 4x = 0, isa)3b)5c)7d)9Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x = cos 3x + cos 4x = 0, isa)3b)5c)7d)9Correct answer is option 'C'. Can you explain this answer?.
If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x = cos 3x + cos 4x = 0, isa)3b)5c)7d)9Correct answer is option 'C'. 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 If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x = cos 3x + cos 4x = 0, isa)3b)5c)7d)9Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x = cos 3x + cos 4x = 0, isa)3b)5c)7d)9Correct answer is option 'C'. Can you explain this answer?.
Solutions for If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x = cos 3x + cos 4x = 0, isa)3b)5c)7d)9Correct answer is option 'C'. 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 If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x = cos 3x + cos 4x = 0, isa)3b)5c)7d)9Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x = cos 3x + cos 4x = 0, isa)3b)5c)7d)9Correct answer is option 'C'. Can you explain this answer?, a detailed solution for If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x = cos 3x + cos 4x = 0, isa)3b)5c)7d)9Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x = cos 3x + cos 4x = 0, isa)3b)5c)7d)9Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x = cos 3x + cos 4x = 0, isa)3b)5c)7d)9Correct answer is option 'C'. 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup