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Suppose 0 < θ < 90o, then for every θ 4 sin2 θ + 1 is greater than or equal to ?
- a)2
- b)4 sin θ
- c)4 cos θ
- d)4 tan θ
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Suppose 0 < θ < 90o, then for every θ 4 sin2 θ...
We know that,
Arithmetic mean ≥ Geometric mean
(4sin2 θ + 1)/2 ≥
4sin2 θ + 1 ≥ 2. 2 sin θ
4sin2 θ + 1 ≥ 4sin θ
Arithmetic mean ≥ Geometric mean
(4sin2 θ + 1)/2 ≥
4sin2 θ + 1 ≥ 2. 2 sin θ
4sin2 θ + 1 ≥ 4sin θ
Most Upvoted Answer
Suppose 0 < θ < 90o, then for every θ 4 sin2 θ...
We know that,
Arithmetic mean ≥ Geometric mean
(4sin2 θ + 1)/2 ≥
4sin2 θ + 1 ≥ 2. 2 sin θ
4sin2 θ + 1 ≥ 4sin θ
Arithmetic mean ≥ Geometric mean
(4sin2 θ + 1)/2 ≥
4sin2 θ + 1 ≥ 2. 2 sin θ
4sin2 θ + 1 ≥ 4sin θ
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Community Answer
Suppose 0 < θ < 90o, then for every θ 4 sin2 θ...
Explanation:
Given Inequality:
0 < θ="" />< />
Expression to Evaluate:
4 sin^2 θ + 1
Analysis:
- We know that sin^2 θ + cos^2 θ = 1 (Pythagorean identity)
- Rearranging the above identity, we get sin^2 θ = 1 - cos^2 θ
- Substituting sin^2 θ = 1 - cos^2 θ into the expression, we get:
4(1 - cos^2 θ) + 1
= 4 - 4cos^2 θ + 1
= 5 - 4cos^2 θ
Proof:
- To show that 4 sin^2 θ + 1 is greater than or equal to 4 sin θ, we need to compare the expressions.
- 5 - 4cos^2 θ ≥ 4 sin θ
- 5 ≥ 4cos^2 θ + 4 sin θ
- 5 ≥ 4(cos^2 θ + sin θ)
Conclusion:
Therefore, for every θ where 0 < θ="" />< 90o,="" the="" expression="" 4="" sin^2="" θ="" +="" 1="" is="" greater="" than="" or="" equal="" to="" 4="" sin="" θ.="" hence,="" the="" correct="" answer="" is="" option="" 'b'.="" 90o,="" the="" expression="" 4="" sin^2="" θ="" +="" 1="" is="" greater="" than="" or="" equal="" to="" 4="" sin="" θ.="" hence,="" the="" correct="" answer="" is="" option="" />
Given Inequality:
0 < θ="" />< />
Expression to Evaluate:
4 sin^2 θ + 1
Analysis:
- We know that sin^2 θ + cos^2 θ = 1 (Pythagorean identity)
- Rearranging the above identity, we get sin^2 θ = 1 - cos^2 θ
- Substituting sin^2 θ = 1 - cos^2 θ into the expression, we get:
4(1 - cos^2 θ) + 1
= 4 - 4cos^2 θ + 1
= 5 - 4cos^2 θ
Proof:
- To show that 4 sin^2 θ + 1 is greater than or equal to 4 sin θ, we need to compare the expressions.
- 5 - 4cos^2 θ ≥ 4 sin θ
- 5 ≥ 4cos^2 θ + 4 sin θ
- 5 ≥ 4(cos^2 θ + sin θ)
Conclusion:
Therefore, for every θ where 0 < θ="" />< 90o,="" the="" expression="" 4="" sin^2="" θ="" +="" 1="" is="" greater="" than="" or="" equal="" to="" 4="" sin="" θ.="" hence,="" the="" correct="" answer="" is="" option="" 'b'.="" 90o,="" the="" expression="" 4="" sin^2="" θ="" +="" 1="" is="" greater="" than="" or="" equal="" to="" 4="" sin="" θ.="" hence,="" the="" correct="" answer="" is="" option="" />
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Suppose 0 < θ < 90o, then for every θ 4 sin2 θ + 1 is greater than or equal to ?a)2b)4 sin θc)4 cos θd)4 tan θCorrect answer is option 'B'. Can you explain this answer?
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Suppose 0 < θ < 90o, then for every θ 4 sin2 θ + 1 is greater than or equal to ?a)2b)4 sin θc)4 cos θd)4 tan θCorrect answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Suppose 0 < θ < 90o, then for every θ 4 sin2 θ + 1 is greater than or equal to ?a)2b)4 sin θc)4 cos θd)4 tan θCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose 0 < θ < 90o, then for every θ 4 sin2 θ + 1 is greater than or equal to ?a)2b)4 sin θc)4 cos θd)4 tan θCorrect answer is option 'B'. Can you explain this answer?.
Suppose 0 < θ < 90o, then for every θ 4 sin2 θ + 1 is greater than or equal to ?a)2b)4 sin θc)4 cos θd)4 tan θCorrect answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Suppose 0 < θ < 90o, then for every θ 4 sin2 θ + 1 is greater than or equal to ?a)2b)4 sin θc)4 cos θd)4 tan θCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose 0 < θ < 90o, then for every θ 4 sin2 θ + 1 is greater than or equal to ?a)2b)4 sin θc)4 cos θd)4 tan θCorrect answer is option 'B'. Can you explain this answer?.
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