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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Example 3 Show that sinβˆ’1 (2x√(1βˆ’π‘₯2)) = 2 sin-1x Solving L.H.S. sinβˆ’1 ( 2x √(1βˆ’π‘₯2) ) Putting x = sin ΞΈ = sinβˆ’1 ("2 sin ΞΈ " √(πŸβˆ’π’”π’Šπ’πŸ" ΞΈ" )) = sinβˆ’1 ("2 sin ΞΈ " √(π’„π’π’”πŸ" ΞΈ" )) = sinβˆ’1 (2sin ΞΈ cos 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 = 2ΞΈ = 2 Γ— sinβˆ’1 x = 2 sinβˆ’1 x = R.H.S. Since L.H.S. = R. H. S. Hence proved As x = sin ΞΈ sin-1 x = ΞΈ

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.