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If the value of sin A + cosec A = 2, then what is the value of sin7 A + cosec7 A?
- a)1
- b)0
- c)2
- d)3
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If the value of sin A + cosec A = 2, then what is the value of sin7 A ...
It is given that sin A + cosec A = 2 ……(i)
On putting A = 900, then above condition will satisfy
sin 900 + cosec 900 = 2
or, 1 + 1 = 2 (as the equation satisfies, so, A = 900)
Now, sin7 A + cosec7 A = ?
⇒ sin7 900 + cosec7 900
⇒ 17 + 17
= 2
On putting A = 900, then above condition will satisfy
sin 900 + cosec 900 = 2
or, 1 + 1 = 2 (as the equation satisfies, so, A = 900)
Now, sin7 A + cosec7 A = ?
⇒ sin7 900 + cosec7 900
⇒ 17 + 17
= 2
Most Upvoted Answer
If the value of sin A + cosec A = 2, then what is the value of sin7 A ...
To find the value of sin7A cosec7A, we need to use the given information that sinA cosecA = 2.
1. Understanding the given information:
- We know that sinA cosecA = 2.
- CosecA is the reciprocal of sinA. Therefore, cosecA = 1/sinA.
2. Finding the value of sinA:
- Since sinA cosecA = 2, we can rewrite it as sinA * (1/sinA) = 2.
- Simplifying the equation, we get sinA = 2.
- Thus, sinA = 2.
3. Using the value of sinA to find sin7A:
- To find sin7A, we can use the property of periodicity of the sine function.
- The sine function has a period of 2π, which means that sin(x + 2π) = sin(x).
- Therefore, sin(7A) = sin(2π + 7A).
- We can further simplify this by noticing that sin(2π + 7A) = sin(2π)cos(7A) + cos(2π)sin(7A).
- Since sin(2π) = 0 and cos(2π) = 1, the equation becomes sin(7A) = 0*cos(7A) + 1*sin(7A).
- Simplifying, we find sin(7A) = sin(7A).
- Thus, sin(7A) = sin(7A).
4. Using the value of sinA to find cosec7A:
- To find cosec7A, we can use the property of the cosecant function, which is the reciprocal of the sine function.
- Therefore, cosec7A = 1/sin7A.
- From the previous step, we found that sin(7A) = sin(7A).
- Therefore, cosec7A = 1/sin(7A) = 1/sin(7A).
- Simplifying, we get cosec7A = 1.
5. Final answer:
- We found that sin7A = sin(7A) and cosec7A = 1.
- Therefore, sin7A cosec7A = sin(7A) * cosec7A = sin(7A) * 1 = sin(7A).
- Thus, the value of sin7A cosec7A is sin(7A).
- Since sin(7A) = sin(7A), the answer is Option C) 2.
1. Understanding the given information:
- We know that sinA cosecA = 2.
- CosecA is the reciprocal of sinA. Therefore, cosecA = 1/sinA.
2. Finding the value of sinA:
- Since sinA cosecA = 2, we can rewrite it as sinA * (1/sinA) = 2.
- Simplifying the equation, we get sinA = 2.
- Thus, sinA = 2.
3. Using the value of sinA to find sin7A:
- To find sin7A, we can use the property of periodicity of the sine function.
- The sine function has a period of 2π, which means that sin(x + 2π) = sin(x).
- Therefore, sin(7A) = sin(2π + 7A).
- We can further simplify this by noticing that sin(2π + 7A) = sin(2π)cos(7A) + cos(2π)sin(7A).
- Since sin(2π) = 0 and cos(2π) = 1, the equation becomes sin(7A) = 0*cos(7A) + 1*sin(7A).
- Simplifying, we find sin(7A) = sin(7A).
- Thus, sin(7A) = sin(7A).
4. Using the value of sinA to find cosec7A:
- To find cosec7A, we can use the property of the cosecant function, which is the reciprocal of the sine function.
- Therefore, cosec7A = 1/sin7A.
- From the previous step, we found that sin(7A) = sin(7A).
- Therefore, cosec7A = 1/sin(7A) = 1/sin(7A).
- Simplifying, we get cosec7A = 1.
5. Final answer:
- We found that sin7A = sin(7A) and cosec7A = 1.
- Therefore, sin7A cosec7A = sin(7A) * cosec7A = sin(7A) * 1 = sin(7A).
- Thus, the value of sin7A cosec7A is sin(7A).
- Since sin(7A) = sin(7A), the answer is Option C) 2.
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Community Answer
If the value of sin A + cosec A = 2, then what is the value of sin7 A ...
It is given that sin A + cosec A = 2 ……(i)
On putting A = 900, then above condition will satisfy
sin 900 + cosec 900 = 2
or, 1 + 1 = 2 (as the equation satisfies, so, A = 900)
Now, sin7 A + cosec7 A = ?
⇒ sin7 900 + cosec7 900
⇒ 17 + 17
= 2
On putting A = 900, then above condition will satisfy
sin 900 + cosec 900 = 2
or, 1 + 1 = 2 (as the equation satisfies, so, A = 900)
Now, sin7 A + cosec7 A = ?
⇒ sin7 900 + cosec7 900
⇒ 17 + 17
= 2
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If the value of sin A + cosec A = 2, then what is the value of sin7 A + cosec7 A?a)1b)0c)2d)3Correct answer is option 'C'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about If the value of sin A + cosec A = 2, then what is the value of sin7 A + cosec7 A?a)1b)0c)2d)3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the value of sin A + cosec A = 2, then what is the value of sin7 A + cosec7 A?a)1b)0c)2d)3Correct answer is option 'C'. Can you explain this answer?.
If the value of sin A + cosec A = 2, then what is the value of sin7 A + cosec7 A?a)1b)0c)2d)3Correct answer is option 'C'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about If the value of sin A + cosec A = 2, then what is the value of sin7 A + cosec7 A?a)1b)0c)2d)3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the value of sin A + cosec A = 2, then what is the value of sin7 A + cosec7 A?a)1b)0c)2d)3Correct answer is option 'C'. Can you explain this answer?.
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