CLASS XII
MATHEMATICS
HOT PRACTICE TEST
Chapter 2 – Inverse Trigonometric Functions
Higher Order Thinking Practice Test • 25 Marks • 60 Minutes
Concept Graphic – Principal Values
Section A – 6 × 1 = 6
1. Find the principal value of
sin⁻¹(1/2).
2. State the principal-value range of
cos⁻¹x.
3. Evaluate
tan⁻¹1.
4. Is
sin⁻¹(sin 5π/6) equal to
5π/6? Explain briefly.
5. Find the value of
tan⁻¹0.
6. State the domain of
sin⁻¹x.
Section B – 3 × 2 = 6
7. Simplify
sin⁻¹x + cos⁻¹x.
8. Evaluate
tan⁻¹(1/2)+tan⁻¹(1/3).
9. Explain why the inverse of sine requires a restricted domain.
Section C – 3 × 3 = 9
10. Prove that
tan⁻¹x + tan⁻¹(1/x)=π/2
for x>0.
11. Solve
sin⁻¹x = cos⁻¹(2x)
for all permissible real values of x.
12. Simplify
tan⁻¹[(x−1)/(1+x)]
with appropriate restrictions on x.
Section D – 1 × 4 = 4
13. Derive an expression for
tan⁻¹x + tan⁻¹y
and discuss how the result changes according to the signs and magnitude
of xy.