Case Study Class 12 Inverse Trigo Functions

Math Case Study Class 12 Inverse Trigo Functions

Inverse Trigonometry – Free Online Test for Class 12 | Math Case Study Questions

Case Study: Inverse Trigonometric Functions

Ravi, a Class 12 student, is preparing for his final mathematics examination. While studying inverse trigonometric functions, he encounters a variety of problems involving the domain, range, and principal values of these functions. Ravi realizes that understanding the principal value branches and their respective domains is critical in solving such problems correctly.He also learns that many expressions involving inverse trigonometric functions can be simplified using identities such as $\sin^{-1}x + \cos^{-1}x = \frac{\pi}{2}$ and others. The following questions are based on Ravi’s learning journey and the concepts discussed.

1. The value of sin−1(1/2) + cos−1(1/2) is:
✅ Correct Answer: (a)
✔️ Explanation: sin⁻¹x + cos⁻¹x = π/2 for all x ∈ [-1, 1].
2. The principal value of tan−1(√3) is:
✅ Correct Answer: (b)
✔️ Explanation: tan⁻¹(√3) = π/3 since tan(π/3) = √3 and lies in the principal value branch (−π/2, π/2).
3. The domain of sec−1x is:
✅ Correct Answer: (a)
✔️ Explanation: sec⁻¹x is defined for |x| ≥ 1, so domain is (−∞, −1] ∪ [1, ∞).
4. The graph of sin−1x lies within:
✅ Correct Answer: (b)
✔️ Explanation: Domain is [−1,1] and range is [−π/2, π/2].
5. The identity tan−1x + cot−1x equals:
✅ Correct Answer: (b)
✔️ Explanation: For all x > 0, tan⁻¹x + cot⁻¹x = π/2.