SSC Exam > SSC Questions > If sin (A + B) = √3 / 2 and tan (A &nda...
Start Learning for Free
If sin (A + B) = √3 / 2 and tan (A – B) = 1. What are the values of A and B?
- a)37, 54
- b)50, 10
- c)45, 15
- d)52.5, 7.5
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If sin (A + B) = √3 / 2 and tan (A – B) = 1. What are the ...
Free Test
FREE
| Start Free Test |
Community Answer
If sin (A + B) = √3 / 2 and tan (A – B) = 1. What are the ...
Given Information:
- sin(A + B) = √3 / 2
- tan(A – B) = 1
Solution:
Using Trigonometric Identities:
1. Sum and Difference of Angles Formulas:
- sin(A + B) = sinAcosB + cosAsinB
- tan(A - B) = (tanA - tanB) / (1 + tanAtanB)
2. Given Values:
- sin(A + B) = √3 / 2
- tan(A - B) = 1
3. Express sin(A + B) and tan(A - B) in terms of sinA, cosA, sinB, and cosB:
- sin(A + B) = sinAcosB + cosAsinB = √3 / 2
- tan(A - B) = (tanA - tanB) / (1 + tanAtanB) = 1
4. Solving the Equations:
- From sin(A + B) = √3 / 2, we can deduce that A + B = 60°
- From tan(A - B) = 1, we can deduce that A - B = 45°
5. Solving for A and B:
- Adding the equations A + B = 60° and A - B = 45°, we get:
2A = 105°
A = 52.5°
- Substituting the value of A in A + B = 60°, we get:
52.5° + B = 60°
B = 60° - 52.5°
B = 7.5°
Therefore, the values of A and B are 52.5° and 7.5° respectively. The correct answer is option 'D'.
- sin(A + B) = √3 / 2
- tan(A – B) = 1
Solution:
Using Trigonometric Identities:
1. Sum and Difference of Angles Formulas:
- sin(A + B) = sinAcosB + cosAsinB
- tan(A - B) = (tanA - tanB) / (1 + tanAtanB)
2. Given Values:
- sin(A + B) = √3 / 2
- tan(A - B) = 1
3. Express sin(A + B) and tan(A - B) in terms of sinA, cosA, sinB, and cosB:
- sin(A + B) = sinAcosB + cosAsinB = √3 / 2
- tan(A - B) = (tanA - tanB) / (1 + tanAtanB) = 1
4. Solving the Equations:
- From sin(A + B) = √3 / 2, we can deduce that A + B = 60°
- From tan(A - B) = 1, we can deduce that A - B = 45°
5. Solving for A and B:
- Adding the equations A + B = 60° and A - B = 45°, we get:
2A = 105°
A = 52.5°
- Substituting the value of A in A + B = 60°, we get:
52.5° + B = 60°
B = 60° - 52.5°
B = 7.5°
Therefore, the values of A and B are 52.5° and 7.5° respectively. The correct answer is option 'D'.
|
Explore Courses for SSC exam
|
|
Similar SSC Doubts
If sin (A + B) = √3 / 2 and tan (A – B) = 1. What are the values of A and B?a)37, 54b)50, 10c)45, 15d)52.5, 7.5Correct answer is option 'D'. Can you explain this answer?
Question Description
If sin (A + B) = √3 / 2 and tan (A – B) = 1. What are the values of A and B?a)37, 54b)50, 10c)45, 15d)52.5, 7.5Correct answer is option 'D'. Can you explain this answer? for SSC 2025 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about If sin (A + B) = √3 / 2 and tan (A – B) = 1. What are the values of A and B?a)37, 54b)50, 10c)45, 15d)52.5, 7.5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for SSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sin (A + B) = √3 / 2 and tan (A – B) = 1. What are the values of A and B?a)37, 54b)50, 10c)45, 15d)52.5, 7.5Correct answer is option 'D'. Can you explain this answer?.
If sin (A + B) = √3 / 2 and tan (A – B) = 1. What are the values of A and B?a)37, 54b)50, 10c)45, 15d)52.5, 7.5Correct answer is option 'D'. Can you explain this answer? for SSC 2025 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about If sin (A + B) = √3 / 2 and tan (A – B) = 1. What are the values of A and B?a)37, 54b)50, 10c)45, 15d)52.5, 7.5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for SSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sin (A + B) = √3 / 2 and tan (A – B) = 1. What are the values of A and B?a)37, 54b)50, 10c)45, 15d)52.5, 7.5Correct answer is option 'D'. Can you explain this answer?.
Solutions for If sin (A + B) = √3 / 2 and tan (A – B) = 1. What are the values of A and B?a)37, 54b)50, 10c)45, 15d)52.5, 7.5Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for SSC.
Download more important topics, notes, lectures and mock test series for SSC Exam by signing up for free.
Here you can find the meaning of If sin (A + B) = √3 / 2 and tan (A – B) = 1. What are the values of A and B?a)37, 54b)50, 10c)45, 15d)52.5, 7.5Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If sin (A + B) = √3 / 2 and tan (A – B) = 1. What are the values of A and B?a)37, 54b)50, 10c)45, 15d)52.5, 7.5Correct answer is option 'D'. Can you explain this answer?, a detailed solution for If sin (A + B) = √3 / 2 and tan (A – B) = 1. What are the values of A and B?a)37, 54b)50, 10c)45, 15d)52.5, 7.5Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of If sin (A + B) = √3 / 2 and tan (A – B) = 1. What are the values of A and B?a)37, 54b)50, 10c)45, 15d)52.5, 7.5Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If sin (A + B) = √3 / 2 and tan (A – B) = 1. What are the values of A and B?a)37, 54b)50, 10c)45, 15d)52.5, 7.5Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice SSC tests.
|
|
Explore Courses for SSC 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