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All x satisfying the inequality (cot–1 x)2 – 7 (cot–1 x) + 10 > 0, lie in the interval:-
- a)(–∞, cot 5) ∪ (cot 4, cot 2)
- b)(cot 5, cot 4)
- c)(cot 2, ∞)
- d)(–∞, cot 5) ∪ (cot 2, ∞)
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
All x satisfying the inequality (cot–1 x)2 – 7 (cot–...
cot–1x > 5, cot–1x < 2
⇒ x < cot5, x > cot2
⇒ x < cot5, x > cot2
Most Upvoted Answer
All x satisfying the inequality (cot–1 x)2 – 7 (cot–...
Explanation:
Given Inequality:
The given inequality is: (cot⁻¹ x)² – 7(cot⁻¹ x) + 10 > 0
Finding the Roots:
To solve this inequality, we first find the roots of the quadratic equation formed by the given inequality:
(cot⁻¹ x)² – 7(cot⁻¹ x) + 10 = 0
This can be factored as: (cot⁻¹ x - 2)(cot⁻¹ x - 5) > 0
So, the roots are cot 2 and cot 5.
Interval Analysis:
- The inequality is greater than 0, which means we need to find the intervals where the inequality is positive.
- The intervals to consider are (-∞, cot 2), (cot 2, cot 5), and (cot 5, ∞).
Checking the Intervals:
- Checking the interval (-∞, cot 2): For x < cot="" 2,="" the="" inequality="" is="" />
- Checking the interval (cot 2, cot 5): For cot 2 < x="" />< cot="" 5,="" the="" inequality="" is="" not="" />
- Checking the interval (cot 5, ∞): For x > cot 5, the inequality is satisfied.
Final Interval:
The intervals where the inequality (cot⁻¹ x)² – 7(cot⁻¹ x) + 10 > 0 holds true are (-∞, cot 2) and (cot 5, ∞). Therefore, the correct answer is option 'D'.
Given Inequality:
The given inequality is: (cot⁻¹ x)² – 7(cot⁻¹ x) + 10 > 0
Finding the Roots:
To solve this inequality, we first find the roots of the quadratic equation formed by the given inequality:
(cot⁻¹ x)² – 7(cot⁻¹ x) + 10 = 0
This can be factored as: (cot⁻¹ x - 2)(cot⁻¹ x - 5) > 0
So, the roots are cot 2 and cot 5.
Interval Analysis:
- The inequality is greater than 0, which means we need to find the intervals where the inequality is positive.
- The intervals to consider are (-∞, cot 2), (cot 2, cot 5), and (cot 5, ∞).
Checking the Intervals:
- Checking the interval (-∞, cot 2): For x < cot="" 2,="" the="" inequality="" is="" />
- Checking the interval (cot 2, cot 5): For cot 2 < x="" />< cot="" 5,="" the="" inequality="" is="" not="" />
- Checking the interval (cot 5, ∞): For x > cot 5, the inequality is satisfied.
Final Interval:
The intervals where the inequality (cot⁻¹ x)² – 7(cot⁻¹ x) + 10 > 0 holds true are (-∞, cot 2) and (cot 5, ∞). Therefore, the correct answer is option 'D'.
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All x satisfying the inequality (cot–1 x)2 – 7 (cot–1 x) + 10 > 0, lie in the interval:-a)(–∞, cot 5) ∪ (cot 4, cot 2)b)(cot 5, cot 4)c)(cot 2, ∞)d)(–∞, cot 5) ∪ (cot 2, ∞)Correct answer is option 'D'. Can you explain this answer?
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All x satisfying the inequality (cot–1 x)2 – 7 (cot–1 x) + 10 > 0, lie in the interval:-a)(–∞, cot 5) ∪ (cot 4, cot 2)b)(cot 5, cot 4)c)(cot 2, ∞)d)(–∞, cot 5) ∪ (cot 2, ∞)Correct answer is option 'D'. 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 All x satisfying the inequality (cot–1 x)2 – 7 (cot–1 x) + 10 > 0, lie in the interval:-a)(–∞, cot 5) ∪ (cot 4, cot 2)b)(cot 5, cot 4)c)(cot 2, ∞)d)(–∞, cot 5) ∪ (cot 2, ∞)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for All x satisfying the inequality (cot–1 x)2 – 7 (cot–1 x) + 10 > 0, lie in the interval:-a)(–∞, cot 5) ∪ (cot 4, cot 2)b)(cot 5, cot 4)c)(cot 2, ∞)d)(–∞, cot 5) ∪ (cot 2, ∞)Correct answer is option 'D'. Can you explain this answer?.
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