Ex 2.2, 6 - Simplify: tan-1 1/root (x2-1) - Class 12 Inverse - Not clear how to approach

  1. Chapter 2 Class 12 Inverse Trigonometric Functions
  2. Serial order wise
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Ex 2.2, 6 Write the function in the simplest form: tan-1 1/ ( ^2 1), |x| > 1 tan-1 (1/ ( ^2 1)) Putting x = sec = tan-1 (1/ (sec^2 1)) = tan-1 (1/ ( (1 + tan^2 ) 1)) = tan-1 (1/ ( 1 1 + tan^2 )) = tan-1 (1/ (tan^2 )) = tan-1 (1/tan ) = tan-1 (cot ) = tan-1 tan (90 ) = 90 = /2 We assumed x = sec sec = x = sec-1 x Hence tan-1 (1/ ( ^2 1)) = /2 = /2 sec-1 x

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