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If sin A = 8/17, what will be the value of cos A sec A?
- a)2
- b)-1
- c)1
- d)0
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If sin A =8/17, what will be the value of cos A sec A?a)2b)-1c)1d)0Cor...
Given: sin A = 8/17
To find: The value of cos A sec A
We know that the Pythagorean identity states that sin^2 A + cos^2 A = 1. Using this identity, we can find the value of cos A.
1. Find cos A:
Using the Pythagorean identity, we have:
sin^2 A + cos^2 A = 1
(8/17)^2 + cos^2 A = 1
64/289 + cos^2 A = 1
cos^2 A = 289/289 - 64/289
cos^2 A = 225/289
Taking the square root of both sides:
cos A = ±√(225/289)
Since cosine is positive in the first and fourth quadrants, we take the positive value:
cos A = √(225/289)
cos A = 15/17
2. Find sec A:
Secant is the reciprocal of cosine, so:
sec A = 1/cos A
sec A = 1/(15/17)
sec A = 17/15
3. Find the value of cos A sec A:
cos A sec A = (15/17) * (17/15)
cos A sec A = 1
Therefore, the value of cos A sec A is 1.
Hence, the correct answer is option 'C'.
To find: The value of cos A sec A
We know that the Pythagorean identity states that sin^2 A + cos^2 A = 1. Using this identity, we can find the value of cos A.
1. Find cos A:
Using the Pythagorean identity, we have:
sin^2 A + cos^2 A = 1
(8/17)^2 + cos^2 A = 1
64/289 + cos^2 A = 1
cos^2 A = 289/289 - 64/289
cos^2 A = 225/289
Taking the square root of both sides:
cos A = ±√(225/289)
Since cosine is positive in the first and fourth quadrants, we take the positive value:
cos A = √(225/289)
cos A = 15/17
2. Find sec A:
Secant is the reciprocal of cosine, so:
sec A = 1/cos A
sec A = 1/(15/17)
sec A = 17/15
3. Find the value of cos A sec A:
cos A sec A = (15/17) * (17/15)
cos A sec A = 1
Therefore, the value of cos A sec A is 1.
Hence, the correct answer is option 'C'.
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Community Answer
If sin A =8/17, what will be the value of cos A sec A?a)2b)-1c)1d)0Cor...
sin A = 8/17
cos A sec A can be written as
∴ cos A sec A = 1
cos A sec A can be written as
∴ cos A sec A = 1
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If sin A =8/17, what will be the value of cos A sec A?a)2b)-1c)1d)0Correct answer is option 'C'. Can you explain this answer?
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