# 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

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**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:

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