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Direction: Read the following text and answer the following questions on the basis of the same:
The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions.
Principal value of cot-1(√3) is :
  • a)
    π/3
  • b)
    π
  • c)
    π/6
  • d)
    π/2
Correct answer is option 'C'. Can you explain this answer?
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Direction: Read the following text and answer the following questions...
Understanding Principal Values of Inverse Trigonometric Functions
The principal value of an inverse trigonometric function is the value that lies within a specific range, typically chosen to make the function single-valued. For cotangent, the principal value is defined in the range (0, π).
Evaluating cot-1(√3)
To find the principal value of cot-1(√3), we need to determine the angle θ such that:
- cot(θ) = √3
Identifying the Angle
- The cotangent function is defined as the ratio of cosine to sine: cot(θ) = cos(θ)/sin(θ).
- We know that cot(π/6) = √3. This is because:
- In a 30-60-90 triangle, the adjacent side (cos) is √3, and the opposite side (sin) is 1.
Conclusion
- Therefore, when θ = π/6, cot(θ) yields √3.
- Since π/6 lies within the principal value range of (0, π), the answer for cot-1(√3) is indeed:
Correct Answer: Option C - π/6
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Direction: Read the following text and answer the following questions...
Cot -1(√3) =cot-1 (cot (π/6) = π/6
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Direction: Read the following text and answer the following questions on the basis of the same:The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions.Principal value of cot-1(√3) is :a)π/3b)πc)π/6d)π/2Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Direction: Read the following text and answer the following questions on the basis of the same:The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions.Principal value of cot-1(√3) is :a)π/3b)πc)π/6d)π/2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: Read the following text and answer the following questions on the basis of the same:The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions.Principal value of cot-1(√3) is :a)π/3b)πc)π/6d)π/2Correct answer is option 'C'. Can you explain this answer?.
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