Finding principal value

Principal Value

Example 1 Important

Ex 2.1, 1

Ex 2.1, 3

Ex 2.1, 10 Important You are here

Ex 2.1, 2

Ex 2.1, 5 Important

Ex 2.1, 9

Ex 2.1, 7 Important

Ex 2.1, 4 Important

Ex 2.1, 6

Ex 2.1, 8 Important

Example 2

Ex 2.2, 10

Example 6 Important

Ex 2.2, 8

Ex 2.2, 11

Misc 2 Important

Ex 2.2, 13 (MCQ) Important

Misc 1

Ex 2.2, 14 (MCQ) Important

Ex 2.2, 15 (MCQ)

Ex 2.1, 12 Important

Ex 2.1, 14 (MCQ) Important

Ex 2.1, 11 Important

Chapter 2 Class 12 Inverse Trigonometric Functions

Concept wise

Last updated at April 16, 2024 by Teachoo

Ex 2.1, 10 (Method 1) Find the principal value of cosec–1 (–√2) Let y = cosec–1 (– √2) y = −cosec–1 (√2) y = − 𝝅/𝟒 Since Range of cosec−1 is [−π/2,π/2] − {0} Hence, Principal Value is (−𝝅)/𝟒 We know that cosec−1 (−x) = − cosec −1 x Since cosec 𝜋/4 = √2 𝜋/4 = cosec−1 (√2) Ex 2.1, 10 (Method 2) Find the principal value of cosec–1 (–√2) Let y = cosec–1 (– √2) cosec y = – √2 cosec y = cosec ((−𝝅)/𝟒) Since Range of cosec−1 is [−π/2,π/2] − {0} Hence, Principal Value is (−𝝅)/𝟒 Rough We know that cosec 45° = √2 θ = 45° = 45 × 𝜋/180 = 𝜋/4 Since −√2 is negative Principal value is − θ i.e. (−𝜋)/4