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If cosθ+cos7θ+cos3θ+cos5θ=0, then θ=
- a)nπ/4
- b)nπ/2
- c)nπ/8
- d)nπ/6
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If cosθ+cos7θ+cos3θ+cos5θ=0, then θ=a)n&...
Given Equation:
cosθ + cos7θ + cos3θ + cos5θ = 0
Solution:
Using the Sum to Product Formula:
We know that cosA + cosB = 2cos((A+B)/2)cos((A-B)/2)
Therefore, we can rewrite the given equation as:
2cos4θcos3θ + 2cos4θcosθ = 0
2cos4θ(cos3θ + cosθ) = 0
Using the Given Equation:
Since the given equation is cosθ + cos7θ + cos3θ + cos5θ = 0, we can rearrange the terms to get:
cosθ + cos3θ + cos5θ + cos7θ = 0
(cosθ + cos7θ) + (cos3θ + cos5θ) = 0
2cos4θ(cos3θ + cosθ) = 0
Conclusion:
Comparing the two expressions we derived, we find that:
2cos4θ(cos3θ + cosθ) = 2cos4θ(cos3θ + cosθ) = 0
This implies that either cos4θ = 0 or cos3θ + cosθ = 0
Final Step:
Since cos4θ = 0 implies θ = nπ/2, and cos3θ + cosθ = 0 implies θ = nπ/8, the correct answer is θ = nπ/8. Therefore, option C is the correct choice.
cosθ + cos7θ + cos3θ + cos5θ = 0
Solution:
Using the Sum to Product Formula:
We know that cosA + cosB = 2cos((A+B)/2)cos((A-B)/2)
Therefore, we can rewrite the given equation as:
2cos4θcos3θ + 2cos4θcosθ = 0
2cos4θ(cos3θ + cosθ) = 0
Using the Given Equation:
Since the given equation is cosθ + cos7θ + cos3θ + cos5θ = 0, we can rearrange the terms to get:
cosθ + cos3θ + cos5θ + cos7θ = 0
(cosθ + cos7θ) + (cos3θ + cos5θ) = 0
2cos4θ(cos3θ + cosθ) = 0
Conclusion:
Comparing the two expressions we derived, we find that:
2cos4θ(cos3θ + cosθ) = 2cos4θ(cos3θ + cosθ) = 0
This implies that either cos4θ = 0 or cos3θ + cosθ = 0
Final Step:
Since cos4θ = 0 implies θ = nπ/2, and cos3θ + cosθ = 0 implies θ = nπ/8, the correct answer is θ = nπ/8. Therefore, option C is the correct choice.
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If cosθ+cos7θ+cos3θ+cos5θ=0, then θ=a)nπ/4b)nπ/2c)nπ/8d)nπ/6Correct answer is option 'C'. Can you explain this answer?
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If cosθ+cos7θ+cos3θ+cos5θ=0, then θ=a)nπ/4b)nπ/2c)nπ/8d)nπ/6Correct answer is option 'C'. 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 If cosθ+cos7θ+cos3θ+cos5θ=0, then θ=a)nπ/4b)nπ/2c)nπ/8d)nπ/6Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If cosθ+cos7θ+cos3θ+cos5θ=0, then θ=a)nπ/4b)nπ/2c)nπ/8d)nπ/6Correct answer is option 'C'. Can you explain this answer?.
If cosθ+cos7θ+cos3θ+cos5θ=0, then θ=a)nπ/4b)nπ/2c)nπ/8d)nπ/6Correct answer is option 'C'. 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 If cosθ+cos7θ+cos3θ+cos5θ=0, then θ=a)nπ/4b)nπ/2c)nπ/8d)nπ/6Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If cosθ+cos7θ+cos3θ+cos5θ=0, then θ=a)nπ/4b)nπ/2c)nπ/8d)nπ/6Correct answer is option 'C'. Can you explain this answer?.
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