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If cos A = 3/5 and sin B = 5/13, find the value of tan (A + B) is
- a)63/16
- b)53/14
- c)23/63
- d)27/24
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If cos A = 3/5 and sin B = 5/13, find the value of tan (A + B) isa)63/...
As per the given data,
Given that cos A = 3/5
4/5 and tan A = SinA/CosA = 4/3
Also given that sin B = 5/13
12/13 and tan B = SinB/CosB = 5/12
We know that
Given that cos A = 3/5
4/5 and tan A = SinA/CosA = 4/3Also given that sin B = 5/13
12/13 and tan B = SinB/CosB = 5/12We know that
Most Upvoted Answer
If cos A = 3/5 and sin B = 5/13, find the value of tan (A + B) isa)63/...
Given: cos A = 3/5 and sin B = 5/13
To find: value of tan (A + B)
Solution:
We know that:
- tan (A + B) = (tan A + tan B) / (1 - tan A tan B)
Now, we need to find the values of tan A and tan B.
Using the Pythagorean identity, we can find the value of sin A:
- sin^2 A + cos^2 A = 1
- sin^2 A = 1 - cos^2 A
- sin A = √(1 - cos^2 A) = √(1 - 9/25) = 4/5
Using the Pythagorean identity, we can find the value of cos B:
- sin^2 B + cos^2 B = 1
- cos^2 B = 1 - sin^2 B
- cos B = √(1 - sin^2 B) = √(1 - 25/169) = 12/13
Now, we can find the values of tan A and tan B:
- tan A = sin A / cos A = (4/5) / (3/5) = 4/3
- tan B = sin B / cos B = (5/13) / (12/13) = 5/12
Substituting the values of tan A and tan B in the formula for tan (A + B), we get:
- tan (A + B) = (tan A + tan B) / (1 - tan A tan B)
- tan (A + B) = (4/3 + 5/12) / (1 - (4/3) * (5/12))
- tan (A + B) = (16/12 + 5/12) / (1 - 5/9)
- tan (A + B) = (21/12) / (4/9)
- tan (A + B) = (21/12) * (9/4)
- tan (A + B) = 63/16
Therefore, the value of tan (A + B) is 63/16. Hence, option A is the correct answer.
To find: value of tan (A + B)
Solution:
We know that:
- tan (A + B) = (tan A + tan B) / (1 - tan A tan B)
Now, we need to find the values of tan A and tan B.
Using the Pythagorean identity, we can find the value of sin A:
- sin^2 A + cos^2 A = 1
- sin^2 A = 1 - cos^2 A
- sin A = √(1 - cos^2 A) = √(1 - 9/25) = 4/5
Using the Pythagorean identity, we can find the value of cos B:
- sin^2 B + cos^2 B = 1
- cos^2 B = 1 - sin^2 B
- cos B = √(1 - sin^2 B) = √(1 - 25/169) = 12/13
Now, we can find the values of tan A and tan B:
- tan A = sin A / cos A = (4/5) / (3/5) = 4/3
- tan B = sin B / cos B = (5/13) / (12/13) = 5/12
Substituting the values of tan A and tan B in the formula for tan (A + B), we get:
- tan (A + B) = (tan A + tan B) / (1 - tan A tan B)
- tan (A + B) = (4/3 + 5/12) / (1 - (4/3) * (5/12))
- tan (A + B) = (16/12 + 5/12) / (1 - 5/9)
- tan (A + B) = (21/12) / (4/9)
- tan (A + B) = (21/12) * (9/4)
- tan (A + B) = 63/16
Therefore, the value of tan (A + B) is 63/16. Hence, option A is the correct answer.
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If cos A = 3/5 and sin B = 5/13, find the value of tan (A + B) isa)63/16b)53/14c)23/63d)27/24Correct answer is option 'A'. Can you explain this answer?
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