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If cot A = 12/5, then (sin A + cos A) × cosec A is:
- a)12/5
- b)17/5
- c)11/5
- d)2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If cot A = 12/5, then (sin A + cos A) × cosec A is:a)12/5b)17/5c...
⇒ (sin A + cosA) × cosecA = (sinA + cosA) × (1/sinA) = 1 + (cosA/sinA) = 1 + cotA = 1 + (12/5) = 17/5
Most Upvoted Answer
If cot A = 12/5, then (sin A + cos A) × cosec A is:a)12/5b)17/5c...
To find (sin A cos A), we can use the identity sin^2 A + cos^2 A = 1.
First, we need to find sin A and cos A individually.
Given cot A = 12/5, we can use the reciprocal identity cot A = cos A/sin A to find sin A and cos A.
cot A = 12/5
cos A/sin A = 12/5
cos A = 12/5 * sin A
Now, we can substitute this value of cos A into the identity sin^2 A + cos^2 A = 1.
sin^2 A + (12/5 * sin A)^2 = 1
sin^2 A + (144/25) * sin^2 A = 1
(25/25) * sin^2 A + (144/25) * sin^2 A = 1
(169/25) * sin^2 A = 1
sin^2 A = 25/169
sin A = ±sqrt(25/169) = ±5/13
Now, substitute the value of sin A into the equation cos A = 12/5 * sin A to find cos A.
cos A = 12/5 * (±5/13) = ±60/65 = ±12/13
Therefore, (sin A cos A) = (±5/13) * (±12/13) = ±60/169.
First, we need to find sin A and cos A individually.
Given cot A = 12/5, we can use the reciprocal identity cot A = cos A/sin A to find sin A and cos A.
cot A = 12/5
cos A/sin A = 12/5
cos A = 12/5 * sin A
Now, we can substitute this value of cos A into the identity sin^2 A + cos^2 A = 1.
sin^2 A + (12/5 * sin A)^2 = 1
sin^2 A + (144/25) * sin^2 A = 1
(25/25) * sin^2 A + (144/25) * sin^2 A = 1
(169/25) * sin^2 A = 1
sin^2 A = 25/169
sin A = ±sqrt(25/169) = ±5/13
Now, substitute the value of sin A into the equation cos A = 12/5 * sin A to find cos A.
cos A = 12/5 * (±5/13) = ±60/65 = ±12/13
Therefore, (sin A cos A) = (±5/13) * (±12/13) = ±60/169.
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If cot A = 12/5, then (sin A + cos A) × cosec A is:a)12/5b)17/5c)11/5d)2Correct answer is option 'B'. 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 cot A = 12/5, then (sin A + cos A) × cosec A is:a)12/5b)17/5c)11/5d)2Correct answer is option 'B'. 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 cot A = 12/5, then (sin A + cos A) × cosec A is:a)12/5b)17/5c)11/5d)2Correct answer is option 'B'. Can you explain this answer?.
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