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Ex 2.1, 12 - Find valueΒ 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

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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 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.