Ex 2.1, 9 - Chapter 2 Class 12 Inverse Trigonometric Functions

Last updated at Dec. 16, 2024 by

Ex 2.1, 9 - Find principal value of cos-1 (-1/root 2) - Ex 2.1

Ex 2.1, 9 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 2

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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

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo