Observe that this function is defined for all real
numbers, where cos x ≠ – 1; i e , at all odd multiplies of π 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