1
7
cos
cos
is equal to
6
−
π






(A) 7
π6
(B) 5
π6
(C)
π3
(D)
6
π
14 1
1
sin
sin
(
)
3
2
−
π

−
−



  is equal to
(A) 1
2
(B) 1
3
(C) 1
4
(D) 1
15 1
1
tan
3
cot
(
3)
−
−
−
−
 is equal to
(A) π
(B)
−π2
(C) 0
(D) 2 3
Miscellaneous Examples
Example 6 Find the value of 
1
3
sin
(sin
)
5
−
π
Solution We know that 
sin1
(sin )
x
x
−
= Therefore, 
1
3
3
sin
(sin
5)
5
−
π
π
=
But
3
,
5
2 2
π
π π


∉ −



 , which is the principal branch of sin–1 x
However
3
3
2
sin (
)
sin(
)
sin
5
5
5
π
π
π
=
π −
=
 and 2
,
5
2 2
π
π π


∈ −




Therefore
1
1
3
2
2
sin
(sin
)
sin
(sin
)
5
5
5
−
−
π
π
π
=
=
Rationalised 2023-24
INVERSE TRIGONOMETRIC FUNCTIONS     31
Miscellaneous Exercise on Chapter 2
Find the value of the following:
1