JEE Exam > JEE Questions > cosA - cos3A =a)-2 sin2AsinAb)2 sin2A sinAc)-...
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cosA - cos3A =
- a)-2 sin2AsinA
- b)2 sin2A sinA
- c)-2sinAsin2A
- d)2sin Asin2A
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
cosA - cos3A =a)-2 sin2AsinAb)2 sin2A sinAc)-2sinAsin2Ad)2sin Asin2ACo...
Solution:
We know that,
cos(3A) = 4cos^3(A) - 3cos(A)
Therefore,
cos(A) - cos(3A) = cos(A) - [4cos^3(A) - 3cos(A)]
= 4cos^3(A) - 2cos(A)
= 2cos(A)(2cos^2(A) - 1)
= 2cos(A)(cos(2A))
= 2cos(A)(2cos^2(A) - 1)
= 4cos^3(A) - 2cos(A)
= 2cos(A)(2cos^2(A) - 1)
= 2cos(A)(cos(2A))
= 2sin(A)sin(2A)
= 2sin^2(A)cos(A)
= 2sin(A)sin(2A)
Hence, the correct option is (B).
We know that,
cos(3A) = 4cos^3(A) - 3cos(A)
Therefore,
cos(A) - cos(3A) = cos(A) - [4cos^3(A) - 3cos(A)]
= 4cos^3(A) - 2cos(A)
= 2cos(A)(2cos^2(A) - 1)
= 2cos(A)(cos(2A))
= 2cos(A)(2cos^2(A) - 1)
= 4cos^3(A) - 2cos(A)
= 2cos(A)(2cos^2(A) - 1)
= 2cos(A)(cos(2A))
= 2sin(A)sin(2A)
= 2sin^2(A)cos(A)
= 2sin(A)sin(2A)
Hence, the correct option is (B).
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Community Answer
cosA - cos3A =a)-2 sin2AsinAb)2 sin2A sinAc)-2sinAsin2Ad)2sin Asin2ACo...
B and d options are same. only arrangement is different.
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cosA - cos3A =a)-2 sin2AsinAb)2 sin2A sinAc)-2sinAsin2Ad)2sin Asin2ACorrect answer is option 'B'. Can you explain this answer?
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cosA - cos3A =a)-2 sin2AsinAb)2 sin2A sinAc)-2sinAsin2Ad)2sin Asin2ACorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about cosA - cos3A =a)-2 sin2AsinAb)2 sin2A sinAc)-2sinAsin2Ad)2sin Asin2ACorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for cosA - cos3A =a)-2 sin2AsinAb)2 sin2A sinAc)-2sinAsin2Ad)2sin Asin2ACorrect answer is option 'B'. Can you explain this answer?.
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