Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/22) | Q#5

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Question

Solve the equation , giving all solutions in the interval .

Solution

We are given;

We know that ;

Let , then we can write;

Now we have two options.

Since ;

We know that except where  or undefined, therefore;

Using calculator we can find that;

Properties of

Domain

Range

Periodicity

Odd/Even

Translation/

Symmetry

We utilize periodicity property of to find other solutions in the given interval .

               

For;

Only solutions of the given equation within given interval  are;

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