Check sibling questions

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

Last updated at May 26, 2023 by

Ex 2.1, 12 - Find value of cos-1 (1/2) + 2 sin-1 (1/2) - Ex 2.1

Ex 2.1, 12 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 2
Ex 2.1, 12 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 3

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Book a free demo

Transcript

Ex 2.1, 12 Find the value of cos−1 (1/2) + 2 sin−1 (1/2) Solving cos−1 (𝟏/𝟐) Let y = cos−1 (1/2) cos y = (1/2) cos y = cos (𝝅/𝟑) ∴ y = 𝝅/𝟑 Since Range of cos−1 is [0 , 𝜋] Hence, the principal value is 𝝅/𝟑 (Since cos 𝜋/3 = 1/2) Solving sin−1 (𝟏/𝟐) Let y = sin−1 (1/2) sin y = 1/2 sin y = sin (𝝅/𝟔) ∴ y = 𝝅/𝟔 Since Range of sin−1 is [(−𝜋)/2 " , " 𝜋/2] Hence, the Principal Value is 𝝅/𝟔 (Since sin 𝜋/6 = 1/2) Now we have cos−1 1/2 = 𝜋/3 & sin−1 1/2 = 𝜋/6 Solving cos−1 𝟏/𝟐 + 2 sin−1 𝟏/𝟐 = 𝜋/3 + 2 × 𝜋/6 = 𝜋/3 + 𝜋/3 = (𝜋 + 𝜋)/3 = 𝟐𝝅/𝟑

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.