Inverse Trigonometric Functions is Chapter 2 in the NCERT Class 12 Maths book and is considered a high-weightage chapter for both board exams and entrance tests like JEE. This chapter deals with the inverse of standard trigonometric functions such as sine, cosine, and tangent, and how they are defined in specific domains and ranges. The PDF of this chapter is available for free download from the NCERT website, making it easier for students to revise concepts, formulas, and solved examples whenever needed.
I decided to write about this chapter because many students either skip it or mug it up without truly understanding it. I remember struggling with things like principal value branches and composite functions when I first read this chapter. But once I understood how it connects to graphs and real-world angles, it actually became fun. This chapter also forms the base for topics like Differentiation and Integration of inverse trigonometric functions later in the book. So it’s important not just from an exam point of view, but also to build clarity for higher maths. My aim here is to break things down simply and guide you on how to get the correct NCERT PDF.
What You’ll Learn in Chapter 2: Inverse Trigonometric Functions
This chapter explains how to find the inverse of basic trigonometric functions and how to restrict their domains to make them one-to-one. Here are the main concepts covered:
- Meaning of Inverse Trigonometric Functions
How functions like sin⁻¹x, cos⁻¹x, tan⁻¹x are defined and used - Domain and Range of Inverse Functions
For example, sin⁻¹x is defined only when x is between -1 and 1 - Principal Value Branches
This tells us the most common (principal) value of the inverse for a given input - Graphs of Inverse Trigonometric Functions
Sketches that help understand their behaviour and symmetry - Properties and Identities
Such as sin⁻¹x + cos⁻¹x = π/2 and similar standard formulas
These topics may look difficult at first, but they’re quite logical once you understand how they are built on Class 11 trigonometry.
Why You Should Take This Chapter Seriously
This chapter is short but very scoring. Many students skip the proofs and directly jump to solving questions, which is okay for revision but not great for conceptual clarity. Once you get the hang of domain restrictions and principal values, solving identities and simplifications becomes much easier. It’s also an important chapter in calculus because differentiation of inverse trig functions is covered in the next few chapters.
If you’re aiming for high marks or want to prepare for competitive exams, mastering this chapter gives you an edge. You’ll see many one-mark and two-mark questions from this chapter in the board paper. And in JEE, properties of inverse trig functions are often mixed into complex problems.
