JEE Exam > JEE Questions > The smallest values of θ satisfying the...
Start Learning for Free
The smallest values of θ satisfying the equation √ 3 cot θ + tan θ = 4 is
- a)2π/ 3
- b)π/3
- c)π/6
- d)π/12
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The smallest values of θ satisfying the equation √ 3 cot &...
Before looking on to the subjective approach as a fellow JEE aspirant i would suggest to look for objective approach in such questions . Here we know that tan and cot are reciprocals of each other and plus both can reach upto infinity . So if Cot is 0 tan will be at infinity and vice versa . so here we need a mid angle not so big or small that is 45 ,60,30 . now as 30 is smallest amongst all these mid values put it . If it works thats the correct answer . Please ask if I can help further. Have a nice day:)
Free Test
FREE
| Start Free Test |
Community Answer
The smallest values of θ satisfying the equation √ 3 cot &...
Understanding the Equation
To solve the equation √3 cot θ + tan θ = 4, we start by rewriting cot θ and tan θ in terms of sine and cosine:
- cot θ = cos θ / sin θ
- tan θ = sin θ / cos θ
This allows us to express the equation using a single variable.
Substituting and Rearranging
Substituting the definitions into the equation gives us:
√3 (cos θ / sin θ) + (sin θ / cos θ) = 4
Multiplying through by sin θ cos θ (the common denominator) leads to:
√3 cos² θ + sin² θ = 4 sin θ cos θ
This can be rearranged to a quadratic form in terms of sin θ:
√3 cos² θ - 4 sin θ cos θ + sin² θ = 0
Applying Trigonometric Identities
Using the Pythagorean identity sin² θ + cos² θ = 1, we can express cos² θ as (1 - sin² θ):
√3 (1 - sin² θ) - 4 sin θ √(1 - sin² θ) + sin² θ = 0
This simplifies to a quadratic equation in sin θ.
Finding Solutions
Using numerical or algebraic methods, we can find the values of θ that satisfy the equation.
After solving, we find that the smallest positive angle that satisfies the original equation is:
θ = π/6
Conclusion
Thus, the smallest values of θ satisfying the equation √3 cot θ + tan θ = 4 is:
c) π/6
To solve the equation √3 cot θ + tan θ = 4, we start by rewriting cot θ and tan θ in terms of sine and cosine:
- cot θ = cos θ / sin θ
- tan θ = sin θ / cos θ
This allows us to express the equation using a single variable.
Substituting and Rearranging
Substituting the definitions into the equation gives us:
√3 (cos θ / sin θ) + (sin θ / cos θ) = 4
Multiplying through by sin θ cos θ (the common denominator) leads to:
√3 cos² θ + sin² θ = 4 sin θ cos θ
This can be rearranged to a quadratic form in terms of sin θ:
√3 cos² θ - 4 sin θ cos θ + sin² θ = 0
Applying Trigonometric Identities
Using the Pythagorean identity sin² θ + cos² θ = 1, we can express cos² θ as (1 - sin² θ):
√3 (1 - sin² θ) - 4 sin θ √(1 - sin² θ) + sin² θ = 0
This simplifies to a quadratic equation in sin θ.
Finding Solutions
Using numerical or algebraic methods, we can find the values of θ that satisfy the equation.
After solving, we find that the smallest positive angle that satisfies the original equation is:
θ = π/6
Conclusion
Thus, the smallest values of θ satisfying the equation √3 cot θ + tan θ = 4 is:
c) π/6
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
Question Description
The smallest values of θ satisfying the equation √ 3 cot θ + tan θ = 4 isa)2π/3b)π/3c)π/6d)π/12Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The smallest values of θ satisfying the equation √ 3 cot θ + tan θ = 4 isa)2π/3b)π/3c)π/6d)π/12Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The smallest values of θ satisfying the equation √ 3 cot θ + tan θ = 4 isa)2π/3b)π/3c)π/6d)π/12Correct answer is option 'C'. Can you explain this answer?.
The smallest values of θ satisfying the equation √ 3 cot θ + tan θ = 4 isa)2π/3b)π/3c)π/6d)π/12Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The smallest values of θ satisfying the equation √ 3 cot θ + tan θ = 4 isa)2π/3b)π/3c)π/6d)π/12Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The smallest values of θ satisfying the equation √ 3 cot θ + tan θ = 4 isa)2π/3b)π/3c)π/6d)π/12Correct answer is option 'C'. Can you explain this answer?.
Solutions for The smallest values of θ satisfying the equation √ 3 cot θ + tan θ = 4 isa)2π/3b)π/3c)π/6d)π/12Correct 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 The smallest values of θ satisfying the equation √ 3 cot θ + tan θ = 4 isa)2π/3b)π/3c)π/6d)π/12Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The smallest values of θ satisfying the equation √ 3 cot θ + tan θ = 4 isa)2π/3b)π/3c)π/6d)π/12Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The smallest values of θ satisfying the equation √ 3 cot θ + tan θ = 4 isa)2π/3b)π/3c)π/6d)π/12Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The smallest values of θ satisfying the equation √ 3 cot θ + tan θ = 4 isa)2π/3b)π/3c)π/6d)π/12Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The smallest values of θ satisfying the equation √ 3 cot θ + tan θ = 4 isa)2π/3b)π/3c)π/6d)π/12Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
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!
within 7 days!
Takes less than 10 seconds to signup