Class 12 Maths Inverse Trigonometric Functions Inverse of tan function

Inverse of tan function

  • Natural domain & Range of tan function: tan : R – { x : x = (2n + 1) π/2, n Z} → R
  • If we restrict domain to [-π/2, π/2], then it becomes one-one & onto with range R.
  • Restricted domain & range of tan function, tan: [-π/2, π/2] → R
  • Restricted domain & range of tan-1 function, tan-1: R à [-π/2, π/2]
  • Actually, tan function restricted to any of the intervals [−3π/2, -π/2 ], to [π/2, 3π/2 ] etc., is one-one & its range is R . Corresponding to each such interval, we get a branch of function tan–1. The branch with range , [-π/2, π/2], is called principal value branch
  • If y = tan–1 x, then tan y = x. Thus, the graph of tan–1 function can be obtained from the graph of original function by interchanging x and y axes, i.e., if (a, b) is a point on  the graph of tan-1 function, then (b, a) becomes the corresponding point on the graph of inverse of tan function

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