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

  1. Chapter 2 Class 12 Inverse Trigonometric Functions
  2. Serial order wise

Transcript

Ex 2.1, 12 Find the value of cosβˆ’1 (1/2) + 2 sinβˆ’1 (1/2) Solving cosβˆ’1 (𝟏/𝟐) Let y = cosβˆ’1 (1/2) cos y = (1/2) cos y = cos (𝝅/πŸ‘) ∴ y = 𝝅/πŸ‘ Since Range of cosβˆ’1 is [0 , πœ‹] Hence, the principal value is 𝝅/πŸ‘ (Since cos πœ‹/3 = 1/2) Solving sinβˆ’1 (𝟏/𝟐) Let y = sinβˆ’1 (1/2) sin y = 1/2 sin y = sin (𝝅/πŸ”) ∴ y = 𝝅/πŸ” Since Range of sinβˆ’1 is [(βˆ’πœ‹)/2 " , " πœ‹/2] Hence, the Principal Value is 𝝅/πŸ” (Since sin πœ‹/6 = 1/2) Now we have cosβˆ’1 1/2 = πœ‹/3 & sinβˆ’1 1/2 = πœ‹/6 Solving cosβˆ’1 𝟏/𝟐 + 2 sinβˆ’1 𝟏/𝟐 = πœ‹/3 + 2 Γ— πœ‹/6 = πœ‹/3 + πœ‹/3 = (πœ‹ + πœ‹)/3 = πŸπ…/πŸ‘

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.