Railways Exam > Railways Questions > If cosec θ = x + 1/4x, then the value of c...
Start Learning for Free
If cosec θ = x + 1/4x, then the value of cosec θ + cot θ is:
- a)-2x
- b)2x
- c)1/2x
- d)−1/2x
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If cosec θ = x + 1/4x, then the value of cosec θ + cot θ is:a)-2xb)...
Let cosec θ + cot θ = k
⇒ cosec θ - cot θ = 1/k
On adding, we get
2 cosec θ = k + 1/k = 2(x+1/4x) = k+1/k
⇒ 2x+1/2x = k+1/k ⇒ k = 2x
Free Test
FREE
| Start Free Test |
Community Answer
If cosec θ = x + 1/4x, then the value of cosec θ + cot θ is:a)-2xb)...
Given:
cosec θ = x + 1/4x
To find:
cosec θ + cot θ
Solution:
Step 1: Find cot θ
We know that cot θ = 1/tan θ
Since cosec θ = 1/sin θ, we can rewrite it as:
x + 1/4x = 1/sin θ
4x^2 + 1 = 4x/sin θ
4x^2 + 1 = 4x/cos θ
cos θ = 4x/(4x^2 + 1)
Step 2: Find cosec θ + cot θ
cosec θ + cot θ = (1/sin θ) + (cos θ/sin θ)
= (1 + cos θ)/sin θ
= (1 + 4x/(4x^2 + 1))/(4x/(4x^2 + 1))
= (4x^2 + 1 + 4x)/(4x)
= (4x^2 + 4x + 1)/(4x)
Simplify the above expression:
= (2x + 1)^2/(2x * 2)
= (2x + 1)^2/4x
= (4x^2 + 4x + 1)/4x
= 1 + x + 1/4x
= x + 1/4x + 1
Therefore, cosec θ + cot θ = x + 1/4x + 1 = 2x
Hence, the correct answer is option B. 2x.
cosec θ = x + 1/4x
To find:
cosec θ + cot θ
Solution:
Step 1: Find cot θ
We know that cot θ = 1/tan θ
Since cosec θ = 1/sin θ, we can rewrite it as:
x + 1/4x = 1/sin θ
4x^2 + 1 = 4x/sin θ
4x^2 + 1 = 4x/cos θ
cos θ = 4x/(4x^2 + 1)
Step 2: Find cosec θ + cot θ
cosec θ + cot θ = (1/sin θ) + (cos θ/sin θ)
= (1 + cos θ)/sin θ
= (1 + 4x/(4x^2 + 1))/(4x/(4x^2 + 1))
= (4x^2 + 1 + 4x)/(4x)
= (4x^2 + 4x + 1)/(4x)
Simplify the above expression:
= (2x + 1)^2/(2x * 2)
= (2x + 1)^2/4x
= (4x^2 + 4x + 1)/4x
= 1 + x + 1/4x
= x + 1/4x + 1
Therefore, cosec θ + cot θ = x + 1/4x + 1 = 2x
Hence, the correct answer is option B. 2x.
|
Explore Courses for Railways exam
|
|
Similar Railways Doubts
Top Courses for RailwaysView all
Question Description
If cosec θ = x + 1/4x, then the value of cosec θ + cot θ is:a)-2xb)2xc)1/2xd)−1/2xCorrect answer is option 'B'. Can you explain this answer? for Railways 2025 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about If cosec θ = x + 1/4x, then the value of cosec θ + cot θ is:a)-2xb)2xc)1/2xd)−1/2xCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Railways 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If cosec θ = x + 1/4x, then the value of cosec θ + cot θ is:a)-2xb)2xc)1/2xd)−1/2xCorrect answer is option 'B'. Can you explain this answer?.
If cosec θ = x + 1/4x, then the value of cosec θ + cot θ is:a)-2xb)2xc)1/2xd)−1/2xCorrect answer is option 'B'. Can you explain this answer? for Railways 2025 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about If cosec θ = x + 1/4x, then the value of cosec θ + cot θ is:a)-2xb)2xc)1/2xd)−1/2xCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Railways 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If cosec θ = x + 1/4x, then the value of cosec θ + cot θ is:a)-2xb)2xc)1/2xd)−1/2xCorrect answer is option 'B'. Can you explain this answer?.
Solutions for If cosec θ = x + 1/4x, then the value of cosec θ + cot θ is:a)-2xb)2xc)1/2xd)−1/2xCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Railways.
Download more important topics, notes, lectures and mock test series for Railways Exam by signing up for free.
Here you can find the meaning of If cosec θ = x + 1/4x, then the value of cosec θ + cot θ is:a)-2xb)2xc)1/2xd)−1/2xCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If cosec θ = x + 1/4x, then the value of cosec θ + cot θ is:a)-2xb)2xc)1/2xd)−1/2xCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for If cosec θ = x + 1/4x, then the value of cosec θ + cot θ is:a)-2xb)2xc)1/2xd)−1/2xCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of If cosec θ = x + 1/4x, then the value of cosec θ + cot θ is:a)-2xb)2xc)1/2xd)−1/2xCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If cosec θ = x + 1/4x, then the value of cosec θ + cot θ is:a)-2xb)2xc)1/2xd)−1/2xCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Railways tests.
|
|
Explore Courses for Railways exam
|
|
Signup to solve all Doubts
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