Example 3 (i) - Chapter 2 Class 12 Inverse Trigonometric Functions

Last updated at Dec. 16, 2024 by Teachoo

Example 3 - Show that sin^-1 (2x√(1-x^2)) = 2 sin^-1 x (Class 12) - Examples

part 2 - Example 3 (i) - Examples - Serial order wise - Chapter 2 Class 12 Inverse Trigonometric Functions

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Transcript

Example 3 Show that sin−1 (2x√(1−𝑥2)) = 2 sin-1x Solving L.H.S. sin−1 ( 2x √(1−𝑥2) ) Putting x = sin θ = sin−1 ("2 sin θ " √(𝟏−𝒔𝒊𝒏𝟐" θ" )) = sin−1 ("2 sin θ " √(𝒄𝒐𝒔𝟐" θ" )) = sin−1 (2sin θ cos θ) = sin−1 (sin 2θ) We need to make 2x √(𝟏−𝒙𝟐) in terms of sin When we get √(1−𝑥2) , we put x = cos θ or sin θ = 2θ = 2 × sin−1 x = 2 sin−1 x = R.H.S. Since L.H.S. = R. H. S. Hence proved As x = sin θ sin-1 x = θ

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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