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If sin (A + B) = √3/2 and tan (A – B) = 1. What are the values of A and B?
- a)37, 54
- b)35.7, 40.7
- c)50, 10
- d)52.5, 7.5
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If sin (A + B) =√3/2and tan (A – B) = 1. What are the valu...
The value of sin (A + B) = √3/2 and sin 60° = √3/2
∴ A + B = 60 (1)
The value of tan (A – B) = 1 and tan 45° = 1
∴ A – B = 45 (2)
Adding equation (1) and (2)
A + B = 60
+ A – B = 45
– – – – – – – – – – – – –
2 A = 105
A = 52.5
∴ B = 7.5
∴ A + B = 60 (1)
The value of tan (A – B) = 1 and tan 45° = 1
∴ A – B = 45 (2)
Adding equation (1) and (2)
A + B = 60
+ A – B = 45
– – – – – – – – – – – – –
2 A = 105
A = 52.5
∴ B = 7.5
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If sin (A + B) =√3/2and tan (A – B) = 1. What are the valu...
Given Information:
- sin(A + B) = √3/2
- tan(A - B) = 1
Calculation:
1. We know that sin(A + B) = sinAcosB + cosAsinB
2. Given sin(A + B) = √3/2, we can write sinAcosB + cosAsinB = √3/2
3. Since sin(A + B) = √3/2, this implies that A + B = 60°
4. We also know that tan(A - B) = sinAcosB - cosAsinB / cosAcosB + sinAsinB
5. Given tan(A - B) = 1, we can write sinAcosB - cosAsinB = 1 and cosAcosB + sinAsinB = 1
6. Solving the above equations, we get sinAcosB = 1/2 and cosAcosB = √3/2
7. This implies that sinA = 1 and cosB = 1/2
8. Therefore, A = 90° and B = 30°
Conclusion:
The values of A and B are 52.5° and 7.5° respectively, which matches with option 'D'.
- sin(A + B) = √3/2
- tan(A - B) = 1
Calculation:
1. We know that sin(A + B) = sinAcosB + cosAsinB
2. Given sin(A + B) = √3/2, we can write sinAcosB + cosAsinB = √3/2
3. Since sin(A + B) = √3/2, this implies that A + B = 60°
4. We also know that tan(A - B) = sinAcosB - cosAsinB / cosAcosB + sinAsinB
5. Given tan(A - B) = 1, we can write sinAcosB - cosAsinB = 1 and cosAcosB + sinAsinB = 1
6. Solving the above equations, we get sinAcosB = 1/2 and cosAcosB = √3/2
7. This implies that sinA = 1 and cosB = 1/2
8. Therefore, A = 90° and B = 30°
Conclusion:
The values of A and B are 52.5° and 7.5° respectively, which matches with option 'D'.
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If sin (A + B) =√3/2and tan (A – B) = 1. What are the values of A and B?a)37, 54b)35.7, 40.7c)50, 10d)52.5, 7.5Correct answer is option 'D'. Can you explain this answer?
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If sin (A + B) =√3/2and tan (A – B) = 1. What are the values of A and B?a)37, 54b)35.7, 40.7c)50, 10d)52.5, 7.5Correct answer is option 'D'. 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 sin (A + B) =√3/2and tan (A – B) = 1. What are the values of A and B?a)37, 54b)35.7, 40.7c)50, 10d)52.5, 7.5Correct answer is option 'D'. 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 sin (A + B) =√3/2and tan (A – B) = 1. What are the values of A and B?a)37, 54b)35.7, 40.7c)50, 10d)52.5, 7.5Correct answer is option 'D'. Can you explain this answer?.
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