Ex 2.1, 6 - Chapter 2 Class 12 Inverse Trigonometric Functions

Last updated at Dec. 16, 2024 by

Ex 2.1, 6 - Find principal value of tan-1 (-1) - Chapter 2 Inverse

Ex 2.1, 6 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 2

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Ex 2.1, 6 (Method 1) Find the principal value of tan−1 (−1) Let y = tan−1 (−1) y = − tan−1 (1) y = − 𝝅/𝟒 Since Range of tan−1 is (−π/2,π/2) Hence, Principal Value of is (−𝝅)/𝟒 We know that tan−1 (−x) = − tan −1 x Since tan 𝜋/4 = 1 𝜋/4 = tan−1 (1) Ex 2.1, 6 (Method 2) Find the principal value of tan−1 (−1) Let y = tan−1 (−1) tan y = −1 tan y = tan ((−𝝅)/𝟒) Since Range of tan−1 is (−π/2,π/2) Hence, Principal Value of is (−𝝅)/𝟒 Rough We know that tan 45° = 1 θ = 45° = 45 × 𝜋/180 = 𝜋/4 Since −1 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