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Last updated at April 16, 2024 by Teachoo
Example 3 Show that sinโ1 (2xโ(1โ๐ฅ2)) = 2 sin-1x Solving L.H.S. sinโ1 ( 2x โ(1โ๐ฅ2) ) Putting x = sin ฮธ = sinโ1 ("2 sin ฮธ " โ(๐โ๐๐๐๐" ฮธ" )) = sinโ1 ("2 sin ฮธ " โ(๐๐๐๐" ฮธ" )) = sinโ1 (2sin ฮธ cos ฮธ) = sinโ1 (sin 2ฮธ) We need to make 2x โ(๐โ๐๐) in terms of sin When we get โ(1โ๐ฅ2) , we put x = cos ฮธ or sin ฮธ = 2ฮธ = 2 ร sinโ1 x = 2 sinโ1 x = R.H.S. Since L.H.S. = R. H. S. Hence proved As x = sin ฮธ sin-1 x = ฮธ