# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | Oct-Nov | (P2-9709/23) | Q#4

Hits: 48

**Question**

** i. **Find

** ii. **Given that

find the value of the positive constant a.

**Solution**

** i.
**

We are required to find;

We have the trigonometric identity;

It can be rearranged as;

Therefore;

provided that

It can be rearranged as;

Therefore;

Rule for integration of is:

Rule for integration of is:

Rule for integration of is:

** ii.
**

We are given that;

Rule for integration of is:

Since ;

Power Rule;

and are inverse functions. The composite function is an identity function, with

domain the positive real numbers. Therefore;

Taking anti-logarithm of both sides;

## Comments