Finding principal value

Principal Value

Example 1 Important

Ex 2.1, 1

Ex 2.1, 3

Ex 2.1, 10 Important

Ex 2.1, 2

Ex 2.1, 5 Important

Ex 2.1, 9 You are here

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, 9 (Method 1) Find the principal value of cos-1 (−1/√2) Let y = cos-1 ((−1)/√2) y = 𝜋 − cos-1 (1/√2) y = 𝜋 − 𝝅/𝟒 y = 𝟑𝝅/𝟒 Since Range of cos-1 is [0 , 𝜋] Hence, the Principal Value is 𝟑𝝅/𝟒 We know that cos−1 (−x) = 𝜋 − cos−1 x Since cos 𝜋/4 = 1/√2 𝜋/4 = cos−1 (1/√2) Ex 2.1, 9 (Method 2) Find the principal value of cos-1 (−1/√2) Let y = cos-1 (−1/√2) cos y = (−1)/√2 cos y = cos (𝟑𝝅/𝟒) Since Range of cos-1 is [0 , 𝜋] Hence, the Principal Value is 𝟑𝝅/𝟒 Rough We know that cos 45° = 1/√2 θ = 45° = 45 × 𝜋/180 = 𝜋/4 Since −1/√2 is negative Principal value is π – θ i.e. π – 𝜋/4 = 3𝜋/4