Ex 2.1, 10 - Chapter 2 Class 12 Inverse Trigonometric Functions

Last updated at Dec. 16, 2024 by

Ex 2.1, 10 - Find principal value of cosec-1 (- root 2) - Ex 2.1

Ex 2.1, 10 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 2

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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

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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