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If tanA = 15/8 and tanB = 7/24, then tan(A-B)?
- a)304/297
- b)304/425
- c)416/87
- d)87/416
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If tanA = 15/8 and tanB = 7/24, then tan(A-B)?a)304/297b)304/425c)416/...
We know that,
∴ tan(A – B) = 304/297
∴ tan(A – B) = 304/297
Most Upvoted Answer
If tanA = 15/8 and tanB = 7/24, then tan(A-B)?a)304/297b)304/425c)416/...
Understanding the Problem
To find tan(A - B) given tanA and tanB, we use the formula:
tan(A - B) = (tanA - tanB) / (1 + tanA * tanB)
Given Values
- tanA = 15/8
- tanB = 7/24
Calculating tan(A - B)
1. Find tanA - tanB
tanA - tanB = (15/8) - (7/24)
- To subtract, find a common denominator (24):
tanA = (15 * 3) / (8 * 3) = 45/24
tanB = 7/24
So, tanA - tanB = 45/24 - 7/24 = 38/24 = 19/12
2. Find 1 + tanA * tanB
tanA * tanB = (15/8) * (7/24) = 105/192
Therefore, 1 + tanA * tanB = 1 + 105/192
- Convert 1 into a fraction with a common denominator:
1 = 192/192
So, 1 + tanA * tanB = 192/192 + 105/192 = 297/192
3. Plugging into the formula
tan(A - B) = (tanA - tanB) / (1 + tanA * tanB)
= (19/12) / (297/192)
= (19/12) * (192/297)
= (19 * 192) / (12 * 297)
4. Simplifying the Expression
- Calculate 19 * 192 = 3648
- Calculate 12 * 297 = 3564
Therefore, tan(A - B) = 3648 / 3564
5. Final Simplification
- Simplifying 3648 / 3564 gives us 304/297.
Conclusion
Thus, the final answer for tan(A - B) is 304/297, which corresponds to option "A".
To find tan(A - B) given tanA and tanB, we use the formula:
tan(A - B) = (tanA - tanB) / (1 + tanA * tanB)
Given Values
- tanA = 15/8
- tanB = 7/24
Calculating tan(A - B)
1. Find tanA - tanB
tanA - tanB = (15/8) - (7/24)
- To subtract, find a common denominator (24):
tanA = (15 * 3) / (8 * 3) = 45/24
tanB = 7/24
So, tanA - tanB = 45/24 - 7/24 = 38/24 = 19/12
2. Find 1 + tanA * tanB
tanA * tanB = (15/8) * (7/24) = 105/192
Therefore, 1 + tanA * tanB = 1 + 105/192
- Convert 1 into a fraction with a common denominator:
1 = 192/192
So, 1 + tanA * tanB = 192/192 + 105/192 = 297/192
3. Plugging into the formula
tan(A - B) = (tanA - tanB) / (1 + tanA * tanB)
= (19/12) / (297/192)
= (19/12) * (192/297)
= (19 * 192) / (12 * 297)
4. Simplifying the Expression
- Calculate 19 * 192 = 3648
- Calculate 12 * 297 = 3564
Therefore, tan(A - B) = 3648 / 3564
5. Final Simplification
- Simplifying 3648 / 3564 gives us 304/297.
Conclusion
Thus, the final answer for tan(A - B) is 304/297, which corresponds to option "A".
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If tanA = 15/8 and tanB = 7/24, then tan(A-B)?a)304/297b)304/425c)416/87d)87/416Correct answer is option 'A'. 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 tanA = 15/8 and tanB = 7/24, then tan(A-B)?a)304/297b)304/425c)416/87d)87/416Correct answer is option 'A'. 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 tanA = 15/8 and tanB = 7/24, then tan(A-B)?a)304/297b)304/425c)416/87d)87/416Correct answer is option 'A'. Can you explain this answer?.
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