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 Rationalised 2023-24
 28
MATHEMATICS
We now consider some examples Example 3 Show that
(i)
sin–1 (
2)
2
x1
−x
 = 2 sin–1 x, 
1
1
2
2
x
−
≤
≤
(ii)
sin–1 (
2)
2
x1
−x
 = 2 cos–1 x, 
1
1
2
≤x
≤
Solution
(i)
Let x = sin θ Then sin–1 x = θ