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

  1. Chapter 2 Class 12 Inverse Trigonometric Functions
  2. Serial order wise
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Example 3 Show that sin-1 (2x√(1 −𝑥2)) = 2 sin-1x Taking 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 = 2θ = 2 × sin-1 x = 2 sin-1 x = R.H.S. Hence L.H.S. = R. H. S. Hence proved Example 3 Show that (ii) sin-1 (2x√(1 −𝑥2)) = 2 cos-1x Taking 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 = 2θ = 2 × cos-1 x = 2 cos-1 x = R.H.S. Hence L.H.S. = R. H. S. Hence proved

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