# Plus Two Maths Notes Chapter 2 Inverse Trigonometric Functions

Students can Download Chapter 2 Inverse Trigonometric Functions Notes, Plus Two Maths Notes helps you to revise the complete Kerala State Syllabus and score more marks in your examinations.

## Kerala Plus Two Maths Notes Chapter 2 Inverse Trigonometric Functions

Introduction
Trigonometric functions are real functions which are not objective and thus its inverse does not exist. In this chapter we study about the restrictions on domains and ranges of trigonometric functions which ensure the existence of their inverse and observe its graphical peculiarities.

A. Concepts
I. Functions
sin-1 x : [-1, 1 ] → [-$$\frac{\pi}{2}$$, $$\frac{\pi}{2}$$]
cos-1 x: [-1, 1] → [0, π]
tan-1 x : R → $$\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$$
cosec-1 x : R – (-1, 1) → [-$$\frac{\pi}{2}$$, $$\frac{\pi}{2}$$] – {0}
sec-1 x : R -(-1, 1) → [0, π] – {$$\frac{\pi}{2}$$}
cot-1 x : R → (0, π)

II. Properties
1. sin (sin-1 x) = x, x ∈ [-1, 1]
sin-1(sinx) = x, x ∈ [-$$\frac{\pi}{2}$$, $$\frac{\pi}{2}$$]
cos(cos-1 x) = x, x ∈ [-1, 1]
cos-1(cosx) = x, x ∈ [o, π]
tan(tan-1 x) = x, x ∈ R
tan-1(tan x) = x, x ∈ $$\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$$

2. sin-1(-x) = -sin-1(x), x ∈ [-1, 1]
tan-1(-x) = -tan-1(x), x ∈ R
cosec-1(-x) = -cosec-1(x), x ∈ R -(-1, 1)
cos-1(-x) = π – cos-1(x), x ∈ [-1, 1]
cot-1(-x) = π – cot-1(x), x ∈ R
sec-1(-x) = π – sec-1(x), x ∈ R -(-1, 1)
sin-1(x) + cos-1(x) = $$\frac{\pi}{2}$$, x ∈ [-1, 1].

3. cosec-1(x) + sec-1(x) = $$\frac{\pi}{2}$$, |x| ≥ 1
tan-1(x) + cot-1(x) = $$\frac{\pi}{2}$$, x ∈ R

4. sin-1 x

5. cos-1 x

6. tan-1(x) + tan-1(y) =

7. tan-1(x) – tan-1(y) =

8. 2 tan-1 x

9. sin-1 x ± sin-1 y