# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2011 | Oct-Nov | (P2-9709/21) | Q#8

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**Question**

**
i. **By first expanding cos(2x + x), show that

** ii. **Hence show that

**Solution**

** i.
**

We are given that and we are required to express as;

Therefore;

We have the trigonometric identity;

From this we can write;

Hence;

** ii.
**

We are required to show that;

We have found in (i) that;

Therefore;

Rule for integration of is:

Rule for integration of is:

Rule for integration of is:

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