Class 12 Inverse Trigonometric Functions Important Questions & PYQs

IMPORTANT MCQ

This section covers MCQs from CBSE Class 12 Mathematics INVERSE TRIGONOMETRY

IMPORTANT 2 MARKS

This section covers 2mark questions from CBSE Class 12 Mathematics INVERSE TRIGONOMETRY

Q10. Evaluate sin⁻¹(sin 3π/4) + cos⁻¹(cos 3π/4) + tan⁻¹(1)

sin⁻¹(√2) = π/4
cos⁻¹(−√2) = 3π/4
tan⁻¹(1) = π/4
Answer: 5π/4

Q11. Evaluate sin⁻¹(sin 3π/4) + cos⁻¹(cos π) + tan⁻¹(1)

sin⁻¹(√2) = π/4
cos⁻¹(−1) = π
tan⁻¹(1) = π/4
Answer: 3π/2

Q12. Range of y = cos⁻¹(x) for x ∈ [−1, 0]

cos⁻¹(x) decreases from π to π/2 as x goes −1 to 0.
Range: [π/2, π]

Q13. Evaluate 3 sin⁻¹(1/√2) + 2 cos⁻¹(√3/2) + cos⁻¹(0)

3 × (π/4) = 3π/4
2 × (π/6) = π/3
cos⁻¹(0) = π/2
Answer: 19π/12

Q14. Domain of y = sin⁻¹(x² − 4)

−1 ≤ x² − 4 ≤ 1 ⇒ 3 ≤ x² ≤ 5
Domain: [−√5, −√3] ∪ [√3, √5]

Q15. Find cos⁻¹(cos(−7π/3))

cos(−7π/3) = cos(π/3) = 1/2
cos⁻¹(1/2) = π/3
Answer: π/3

Q16. Domain and Range of f(x) = tan⁻¹(x)

Domain: ℝ
Range: (−π/2, π/2)

Q17. Range of sin⁻¹(x) for x ∈ [−1/√2, 1/√2]

sin⁻¹(−1/√2) = −π/4
sin⁻¹(1/√2) = π/4
Range: [−π/4, π/4]

3Mark Questions