# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2014 | May-Jun | (P2-9709/21) | Q#5

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**Question**

**
i. **Prove that .

** ii. **Hence

a. Find the exact value of

b. Evaluate

**Solution**

** i.
**

We are given that;

except where or undefined

provided that

We have the trigonometric identity;

Therefore;

Hence;

** ii.
**

**a.
**

We are required to find the exact value of;

As demonstrated in (i);

We can write;

Therefore

**b.
**

We are required to evaluate;

As demonstrated in (i);

Therefore;

Rule for integration of is:

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