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Example 3 Show that sinโˆ’1 (2xโˆš(1โˆ’๐‘ฅ2)) = 2 sin-1x Solving L.H.S. sinโˆ’1 ( 2x โˆš(1โˆ’๐‘ฅ2) ) Putting x = sin ฮธ = sinโˆ’1 ("2 sin ฮธ " โˆš(๐Ÿโˆ’๐’”๐’Š๐’๐Ÿ" ฮธ" )) = sinโˆ’1 ("2 sin ฮธ " โˆš(๐’„๐’๐’”๐Ÿ" ฮธ" )) = sinโˆ’1 (2sin ฮธ cos 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— sinโˆ’1 x = 2 sinโˆ’1 x = R.H.S. Since L.H.S. = R. H. S. Hence proved As x = sin ฮธ sin-1 x = ฮธ

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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.