Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2005 | May-Jun | (P2-9709/02) | Q#7

Hits: 6

 

Question

     i. By expanding , and using double-angle formulae, show that

   ii. Hence, or otherwise, show that

Solution

     i.
 

We have;

We apply following addition formula.

Therefore;

We apply following two formulae.

We have the trigonometric identity;

Therefore, we can replace;

Hence;

   ii.
 

We are required to show that;

As we have demonstrated in (i) that;

Therefore;

Hence;

We now can write the given equation as;

Rule for integration of  is:

Rule for integration of  is:

Rule for integration of  is:

Please follow and like us:
0

Comments