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Example 3 - Show (i) sin-1 (2x/root(1-x2)) = 2 sin-1 x - Examples

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

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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) (As 1 – sin2 θ = cos2 θ) (Using sin 2x = 2 sin x cos x) (Using sin 2x = 2 sin x cos x) = 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

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.