1. Chapter 2 Class 12 Inverse Trigonometric Functions (Term 1)
  2. Concept wise
  3. Formulae based

Example 3 - Chapter 2 Class 12 Inverse Trigonometric Functions (Term 1)

Last updated at Aug. 12, 2021 by

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

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

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  1. Chapter 2 Class 12 Inverse Trigonometric Functions (Term 1)
  2. Concept wise

    3. Formulae based

    Changing of trignometric variables and then applying formula →

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) (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

Chapter 2 Class 12 Inverse Trigonometric Functions (Term 1)
Concept wise

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.