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

Last updated at August 14, 2026 by

Show that sin^-1 (2x √(1-x^2)) = 2 cos^-1 x - Inverse Trigonometry - Examples

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

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Example 3 Show that (ii) sinβˆ’1 (2x√(1βˆ’π‘₯2)) = 2 cosβˆ’1x Solving L.H.S. sinβˆ’1 ( 2x √(1βˆ’π‘₯2) ) Putting x = cos ΞΈ = sinβˆ’1 ("2 cos ΞΈ " √(πŸβˆ’π’„π’π’”πŸ" ΞΈ" )) = sinβˆ’1 ("2 cos ΞΈ " √(π’”π’Šπ’πŸ" ΞΈ" )) = sinβˆ’1 (2 cos ΞΈ sin ΞΈ) = sinβˆ’1 (sin 2ΞΈ) We need to make 2x √(πŸβˆ’π’™πŸ) in terms of sin When we get √(1βˆ’π‘₯2) , we put x = cos ΞΈ or sin ΞΈ

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