SAT Exam > SAT Questions > If tan(α) = 3/4 and tan(β) = 1/3, ...
Start Learning for Free
If tan(α) = 3/4 and tan(β) = 1/3, what is the value of tan(α + β)?
- a)1
- b)13/9
- c)1/2
- d)4/3
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If tan(α) = 3/4 and tan(β) = 1/3, what is the value of tan(...
tan(α + β) = (tan(α) + tan(β))/(1 - tan(α)tan(β))
= (3/4 + 1/3)/(1 - (3/4)(1/3))
= (3/4 + 1/3)/(1 - 1/4)
= (13/12)/(3/4)
= 2.
= (3/4 + 1/3)/(1 - (3/4)(1/3))
= (3/4 + 1/3)/(1 - 1/4)
= (13/12)/(3/4)
= 2.
Free Test
FREE
| Start Free Test |
Community Answer
If tan(α) = 3/4 and tan(β) = 1/3, what is the value of tan(...
Given Information:
- tan(α) = 3/4
- tan(β) = 1/3
Finding tan(α + β):
To find tan(α + β), we will use the formula for the tangent of the sum of two angles:
tan(α + β) = (tan(α) + tan(β)) / (1 - tan(α)tan(β))
Substitute the given values:
tan(α + β) = (3/4 + 1/3) / (1 - (3/4)(1/3))
tan(α + β) = (9/12 + 4/12) / (1 - 1/4)
tan(α + β) = 13/12 / (3/4)
tan(α + β) = 13/12 * 4/3
tan(α + β) = 52/36
tan(α + β) = 13/9
tan(α + β) = 1.44
Therefore, the value of tan(α + β) is 1.44. However, since the answer choices are in fraction form, we need to simplify this decimal to the nearest fraction.
1.44 can be simplified to 4/3.
Therefore, the correct answer is option 'B' (2).
- tan(α) = 3/4
- tan(β) = 1/3
Finding tan(α + β):
To find tan(α + β), we will use the formula for the tangent of the sum of two angles:
tan(α + β) = (tan(α) + tan(β)) / (1 - tan(α)tan(β))
Substitute the given values:
tan(α + β) = (3/4 + 1/3) / (1 - (3/4)(1/3))
tan(α + β) = (9/12 + 4/12) / (1 - 1/4)
tan(α + β) = 13/12 / (3/4)
tan(α + β) = 13/12 * 4/3
tan(α + β) = 52/36
tan(α + β) = 13/9
tan(α + β) = 1.44
Therefore, the value of tan(α + β) is 1.44. However, since the answer choices are in fraction form, we need to simplify this decimal to the nearest fraction.
1.44 can be simplified to 4/3.
Therefore, the correct answer is option 'B' (2).
|
Explore Courses for SAT exam
|
|
Similar SAT Doubts
Top Courses for SATView all
If tan(α) = 3/4 and tan(β) = 1/3, what is the value of tan(α + β)?a)1b)13/9c)1/2d)4/3Correct answer is option 'B'. Can you explain this answer?
Question Description
If tan(α) = 3/4 and tan(β) = 1/3, what is the value of tan(α + β)?a)1b)13/9c)1/2d)4/3Correct answer is option 'B'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about If tan(α) = 3/4 and tan(β) = 1/3, what is the value of tan(α + β)?a)1b)13/9c)1/2d)4/3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If tan(α) = 3/4 and tan(β) = 1/3, what is the value of tan(α + β)?a)1b)13/9c)1/2d)4/3Correct answer is option 'B'. Can you explain this answer?.
If tan(α) = 3/4 and tan(β) = 1/3, what is the value of tan(α + β)?a)1b)13/9c)1/2d)4/3Correct answer is option 'B'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about If tan(α) = 3/4 and tan(β) = 1/3, what is the value of tan(α + β)?a)1b)13/9c)1/2d)4/3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If tan(α) = 3/4 and tan(β) = 1/3, what is the value of tan(α + β)?a)1b)13/9c)1/2d)4/3Correct answer is option 'B'. Can you explain this answer?.
Solutions for If tan(α) = 3/4 and tan(β) = 1/3, what is the value of tan(α + β)?a)1b)13/9c)1/2d)4/3Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for SAT.
Download more important topics, notes, lectures and mock test series for SAT Exam by signing up for free.
Here you can find the meaning of If tan(α) = 3/4 and tan(β) = 1/3, what is the value of tan(α + β)?a)1b)13/9c)1/2d)4/3Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If tan(α) = 3/4 and tan(β) = 1/3, what is the value of tan(α + β)?a)1b)13/9c)1/2d)4/3Correct answer is option 'B'. Can you explain this answer?, a detailed solution for If tan(α) = 3/4 and tan(β) = 1/3, what is the value of tan(α + β)?a)1b)13/9c)1/2d)4/3Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of If tan(α) = 3/4 and tan(β) = 1/3, what is the value of tan(α + β)?a)1b)13/9c)1/2d)4/3Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If tan(α) = 3/4 and tan(β) = 1/3, what is the value of tan(α + β)?a)1b)13/9c)1/2d)4/3Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice SAT tests.
|
|
Explore Courses for SAT 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!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup