Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2003 | May-Jun | (P2-9709/02) | Q#4

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Question

i. Show that the equation

Can be written in the form

ii. Hence solve the equation to

For .

Solution

i.

We are given;

We apply following two addition formulae on both sides of given equation.

Therefore;

Since;

ii.

We are required to solve following equation doe .

We have found in (i) that it can be written as;

Let , then;

Now we have two options.

Since , therefore;

Using calculator we can find that

 

Properties of

Domain

Range

Periodicity

Odd/Even

Translation/

Symmetry

We utilize the periodicity/symmetry property of to find other solutions (roots) of :

Therefore;

For ;

For ;

Only following solutions (roots) are within the given interval ;

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