Class 12 Maths Inverse Trigonometric Functions Inverse of Sec inverse

Inverse of Sec inverse

• Natural domain & Range of sec function: R – { x : x = (2n + 1) π/2, n Z} → R – (– 1, 1)
• If we restrict domain to [0, π] –{π/2}, then it becomes one-one & onto with range R – (–1, 1).
• Restricted domain & range of sec function, sec: [ 0, π ] –{π/2} → R – (–1, 1)
• Restricted domain & range of sec-1 function, sec-1 : R – (–1, 1) à [ 0, π ] –{π/2}
• Actually, sec function restricted to any of the intervals [– π, 0]-{- π/2} , [π, 2π]-{3π/2} , is one-one & its range is R – (–1, 1). Corresponding to each such interval, we get a branch of function sec–1. The branch with range , [0, π ], is called principal value branch
• If y = sec–1 x, then sec y = x.
• Thus, the graph of sec–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 sec-1 function, then (b, a) becomes the corresponding point on the graph of inverse of sec function .