In fact, they will be valid only for some values of x for which
inverse trigonometric functions are defined We will not go into the details of these
values of x in the domain as this discussion goes beyond the scope of this textbook Let us recall that if y = sin–1x, then x = sin y and if x = sin y, then y = sin–1x This
is equivalent to
sin (sin–1 x) = x, x ∈  [– 1, 1] and sin–1 (sin x) = x, x ∈ 
2,
2
−π π





For suitable values of  domain similar results follow for remaining trigonometric
functions