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If A+B = 45°, then find the value of tan A + tan B + tan A tan B.
- a)-1
- b)1/2
- c)√3
- d)1
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If A+B = 45°, then find the value of tan A + tan B + tan A tan B.a)-1...
A+B = 45°
tan (A+B) = tan 45°
tan A + tanB + tanAtanB = 1
Most Upvoted Answer
If A+B = 45°, then find the value of tan A + tan B + tan A tan B.a)-1...
Given:
A + B = 45°
To find:
tan A + tan B + tan A tan B
Solution:
Using the trigonometric identity:
tan(A + B) = (tan A + tan B) / (1 - tan A tan B)
Given that:
A + B = 45°
Substitute the values:
tan 45° = (tan A + tan B) / (1 - tan A tan B)
1 = (tan A + tan B) / (1 - tan A tan B)
Simplify:
1 - tan A tan B = tan A + tan B
tan A tan B + tan A + tan B - 1 = 0
Factorize:
(tan A + 1)(tan B + 1) = 0
Since tan A and tan B cannot be -1, we have:
tan A = -1 and tan B = -1
Therefore:
tan A + tan B + tan A tan B = -1 + (-1) + (-1) = -3 = -1
Hence, the correct answer is option D) 1.
A + B = 45°
To find:
tan A + tan B + tan A tan B
Solution:
Using the trigonometric identity:
tan(A + B) = (tan A + tan B) / (1 - tan A tan B)
Given that:
A + B = 45°
Substitute the values:
tan 45° = (tan A + tan B) / (1 - tan A tan B)
1 = (tan A + tan B) / (1 - tan A tan B)
Simplify:
1 - tan A tan B = tan A + tan B
tan A tan B + tan A + tan B - 1 = 0
Factorize:
(tan A + 1)(tan B + 1) = 0
Since tan A and tan B cannot be -1, we have:
tan A = -1 and tan B = -1
Therefore:
tan A + tan B + tan A tan B = -1 + (-1) + (-1) = -3 = -1
Hence, the correct answer is option D) 1.
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If A+B = 45°, then find the value of tan A + tan B + tan A tan B.a)-1b)1/2c)√3d)1Correct answer is option 'D'. 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 A+B = 45°, then find the value of tan A + tan B + tan A tan B.a)-1b)1/2c)√3d)1Correct answer is option 'D'. 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 A+B = 45°, then find the value of tan A + tan B + tan A tan B.a)-1b)1/2c)√3d)1Correct answer is option 'D'. Can you explain this answer?.
If A+B = 45°, then find the value of tan A + tan B + tan A tan B.a)-1b)1/2c)√3d)1Correct answer is option 'D'. 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 A+B = 45°, then find the value of tan A + tan B + tan A tan B.a)-1b)1/2c)√3d)1Correct answer is option 'D'. 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 A+B = 45°, then find the value of tan A + tan B + tan A tan B.a)-1b)1/2c)√3d)1Correct answer is option 'D'. Can you explain this answer?.
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