sin (tan–1 x), |x| < 1 is equal to
(A)
2
1
x
x
−
(B)
2
1
1
x
−
(C)
2
1
1
x
+
(D)
2
1
x
x
+
14 sin–1 (1 – x) – 2 sin–1 x = 2
π , then x is equal to
(A) 0, 1
2
(B) 1, 1
2
(C) 0
(D) 1
2
Rationalised 2023-24
 32
MATHEMATICS
Summary
® The domains and ranges (principal value branches) of inverse trigonometric
functions are given in the following table:
Functions
Domain
Range
(Principal Value Branches)
y = sin–1 x
[–1, 1]
2,
2
−π π





y = cos–1 x
[–1, 1]
 [0, π]
y = cosec–1 x
R – (–1,1)
2,
2
−π π





– {0}
y = sec–1 x
R – (–1, 1)
[0, π] – { }
2
π
y = tan–1 x
R
,
2 2
π π


−



y = cot–1 x
R
(0, π)
® sin–1x should not be confused with (sin x)–1 In fact (sin x)–1 = 
1
sin x  and
similarly for other trigonometric functions ® The value of an inverse trigonometric functions which lies in its principal
value branch is called the principal value of that inverse trigonometric
functions