We may rewrite this
function as
f(x) =
1
sin
tan
1
cos
x
x
− 



+

=
1
2
2 sin
2cos
2
tan
2cos 2
x
x
x
−
























Rationalised 2023-24
 MATHEMATICS
142
=
tan1
tan 2
2
x
x
− 


 =








Observe that we could cancel cos
x2




 in both numerator and denominator as it
is not equal to zero Thus f ′(x) = 1 2
(iii)
Let f(x) = sin–1 
1
12
4
x
x
+




+
 To find the domain of this function we need to find all
x such that 
21
1
1
1
4
x
x
+
− ≤
≤
+