Given that  `f^{\prime}(x)=\frac{\cos (2 x)}{\sin ^3(2 x)}`  and  , find .   (4 marks)

With a suitable substitution    can be expressed as

Using a suitable substitution,   can be expressed in terms of as

A.  

B.  

C.  

D.  

E.  

Using a suitable substitution, the definite integral    is equivalent to

A.  

B.  

C.  

D.   

E.  

Let  .

Find  and state the largest set of values of for which    is defined.   (3 marks)

Using a suitable substitution,   can be expressed as

A. 

B. 

C.

D.

E.