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

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

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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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.