Example 3 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 3

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Example 3 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 4

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

Transcript

Example 3 Show that (ii) sinโˆ’1 (2xโˆš(1โˆ’๐‘ฅ2)) = 2 cosโˆ’1x Solving L.H.S. sinโˆ’1 ( 2x โˆš(1โˆ’๐‘ฅ2) ) Putting x = cos ฮธ = sinโˆ’1 ("2 cos ฮธ " โˆš(๐Ÿโˆ’๐’„๐’๐’”๐Ÿ" ฮธ" )) = sinโˆ’1 ("2 cos ฮธ " โˆš(๐’”๐’Š๐’๐Ÿ" ฮธ" )) = sinโˆ’1 (2 cos ฮธ sin ฮธ) = sinโˆ’1 (sin 2ฮธ) We need to make 2x โˆš(๐Ÿโˆ’๐’™๐Ÿ) in terms of sin When we get โˆš(1โˆ’๐‘ฅ2) , we put x = cos ฮธ or sin ฮธ = 2ฮธ = 2 ร— cosโˆ’1 x = 2 cosโˆ’1 x = R.H.S. Since L.H.S. = R. H. S. Hence proved As x = cos ฮธ cosโˆ’1 x = ฮธ

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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.