Example 3 (ii) - Chapter 2 Class 12 Inverse Trigonometric Functions
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 3 Show that (ii) sin−1 (2x√(1−𝑥2)) = 2 cos−1x Solving L.H.S. sin−1 ( 2x √(1−𝑥2) ) Putting x = cos θ = sin−1 ("2 cos θ " √(𝟏−𝒄𝒐𝒔𝟐" θ" )) = sin−1 ("2 cos θ " √(𝒔𝒊𝒏𝟐" θ" )) = sin−1 (2 cos θ sin θ) = sin−1 (sin 2θ) We need to make 2x √(𝟏−𝒙𝟐) in terms of sin When we get √(1−𝑥2) , we put x = cos θ or sin θ
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