Chapter 2 Class 12 Inverse Trigonometric Functions

Serial order wise

Last updated at April 16, 2024 by Teachoo

Example 3 Show that sinβ1 (2xβ(1βπ₯2)) = 2 sin-1x Solving L.H.S. sinβ1 ( 2x β(1βπ₯2) ) Putting x = sin ΞΈ = sinβ1 ("2 sin ΞΈ " β(πβππππ" ΞΈ" )) = sinβ1 ("2 sin ΞΈ " β(ππππ" ΞΈ" )) = sinβ1 (2sin ΞΈ cos ΞΈ) = sinβ1 (sin 2ΞΈ) We need to make 2x β(πβππ) in terms of sin When we get β(1βπ₯2) , we put x = cos ΞΈ or sin ΞΈ = 2ΞΈ = 2 Γ sinβ1 x = 2 sinβ1 x = R.H.S. Since L.H.S. = R. H. S. Hence proved As x = sin ΞΈ sin-1 x = ΞΈ