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Which of the following is correct in respect of the equation 3 – tan2θ = α(1 – 3tan2θ)? (Given that α is a real number.)
- a)α ∈ [1/3, 3]
- b)α ∈ (-∝, 1/3] ∪ [3, ∝)
- c)α ∈ (-∝, 1/3) ∪ (3, ∝)
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
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Which of the following is correct in respect of the equation 3 –...
3 – tan2θ = α(1 – 3tan2θ)
⇒ 3tanθ – tan3θ = α(1 – 3tan2θ) × tanθ
⇒ (3tanθ – tan3θ)/(1 – 3tan2θ) = αtanθ
⇒ tan3θ = αtanθ
⇒ sin3θ/cos3θ = αsinθ/cosθ
⇒ sin3θ/sinθ = αcos3θ/cosθ
⇒ (3sinθ – 4sin3θ) /sinθ = α × (4cos3θ – 3cosθ) /cosθ
⇒ 3 – 4sin2θ = α(4cos2θ – 3)
Let sin2θ = t
⇒ cos2θ = 1 – sin2θ = 1 – t
⇒ 3 – 4t = α[4(1 – t) – 3]
⇒ 3 – 4t = α(1 – 4t)
⇒ (4 – 4α)t = 3 – α
⇒ t = (3 – α)/(4 – 4α)
1 ≥ sin2 θ ≥ 0
⇒ 1 ≥ (3 – α)/(4 – 4α) ≥ 0
When 4 – 4α is positve
⇒ 4 – 4α ≥ 3 – α ≥ 0
First inequality
⇒ 4 – 4α ≥ 3 – α
⇒ 1 ≥ 3α
⇒ α ≤ 1/3
When 4 – 4α is negative
⇒ 4 – 4α ≤ 3 – α ≤ 0
⇒ 3 – α ≤ 0
⇒ α ≤ 3
∴ α ∈ (-∝, 1/3] ∪ [3, ∝)
⇒ 3tanθ – tan3θ = α(1 – 3tan2θ) × tanθ
⇒ (3tanθ – tan3θ)/(1 – 3tan2θ) = αtanθ
⇒ tan3θ = αtanθ
⇒ sin3θ/cos3θ = αsinθ/cosθ
⇒ sin3θ/sinθ = αcos3θ/cosθ
⇒ (3sinθ – 4sin3θ) /sinθ = α × (4cos3θ – 3cosθ) /cosθ
⇒ 3 – 4sin2θ = α(4cos2θ – 3)
Let sin2θ = t
⇒ cos2θ = 1 – sin2θ = 1 – t
⇒ 3 – 4t = α[4(1 – t) – 3]
⇒ 3 – 4t = α(1 – 4t)
⇒ (4 – 4α)t = 3 – α
⇒ t = (3 – α)/(4 – 4α)
1 ≥ sin2 θ ≥ 0
⇒ 1 ≥ (3 – α)/(4 – 4α) ≥ 0
When 4 – 4α is positve
⇒ 4 – 4α ≥ 3 – α ≥ 0
First inequality
⇒ 4 – 4α ≥ 3 – α
⇒ 1 ≥ 3α
⇒ α ≤ 1/3
When 4 – 4α is negative
⇒ 4 – 4α ≤ 3 – α ≤ 0
⇒ 3 – α ≤ 0
⇒ α ≤ 3
∴ α ∈ (-∝, 1/3] ∪ [3, ∝)
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Which of the following is correct in respect of the equation 3 –...
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Which of the following is correct in respect of the equation 3 –...
Option B
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Which of the following is correct in respect of the equation 3 – tan2θ = α(1 – 3tan2θ)? (Given that α is a real number.)a)α ∈ [1/3, 3]b)α ∈ (-∝, 1/3] ∪ [3, ∝)c)α ∈ (-∝, 1/3) ∪ (3, ∝)d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
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Which of the following is correct in respect of the equation 3 – tan2θ = α(1 – 3tan2θ)? (Given that α is a real number.)a)α ∈ [1/3, 3]b)α ∈ (-∝, 1/3] ∪ [3, ∝)c)α ∈ (-∝, 1/3) ∪ (3, ∝)d)None of the aboveCorrect 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 Which of the following is correct in respect of the equation 3 – tan2θ = α(1 – 3tan2θ)? (Given that α is a real number.)a)α ∈ [1/3, 3]b)α ∈ (-∝, 1/3] ∪ [3, ∝)c)α ∈ (-∝, 1/3) ∪ (3, ∝)d)None of the aboveCorrect 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 Which of the following is correct in respect of the equation 3 – tan2θ = α(1 – 3tan2θ)? (Given that α is a real number.)a)α ∈ [1/3, 3]b)α ∈ (-∝, 1/3] ∪ [3, ∝)c)α ∈ (-∝, 1/3) ∪ (3, ∝)d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.
Which of the following is correct in respect of the equation 3 – tan2θ = α(1 – 3tan2θ)? (Given that α is a real number.)a)α ∈ [1/3, 3]b)α ∈ (-∝, 1/3] ∪ [3, ∝)c)α ∈ (-∝, 1/3) ∪ (3, ∝)d)None of the aboveCorrect 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 Which of the following is correct in respect of the equation 3 – tan2θ = α(1 – 3tan2θ)? (Given that α is a real number.)a)α ∈ [1/3, 3]b)α ∈ (-∝, 1/3] ∪ [3, ∝)c)α ∈ (-∝, 1/3) ∪ (3, ∝)d)None of the aboveCorrect 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 Which of the following is correct in respect of the equation 3 – tan2θ = α(1 – 3tan2θ)? (Given that α is a real number.)a)α ∈ [1/3, 3]b)α ∈ (-∝, 1/3] ∪ [3, ∝)c)α ∈ (-∝, 1/3) ∪ (3, ∝)d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.
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