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

  1. Chapter 2 Class 12 Inverse Trigonometric Functions
  2. Serial order wise
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Example 3 Show that sin-1 (2x (1 2)) = 2 sin-1x Taking L.H.S. sin-1 ( 2x (1 2) ) Putting x = sin = sin-1 ("2 sin " (1 2" " )) = sin-1 ("2 sin " ( 2" " )) = sin-1 (2sin cos ) = sin-1 sin 2 = 2 = 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 2)) = 2 cos-1x Taking L.H.S. sin-1 ( 2x (1 2) ) Putting x = cos = sin-1 ("2 cos " (1 2" " )) = sin-1 ("2 cos " ( 2" " )) = sin-1 (2 cos sin ) = sin-1 sin 2 = 2 = 2 cos-1 x = 2 cos-1 x = R.H.S. Hence L.H.S. = R. H. S. Hence proved

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