Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2016  FebMar  (P19709/12)  Q#4
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Question
a. Solve the equation , giving the solution in an exact form.
b. Solve, by factorising, the equation for .
Solution
a.
We are given;
b.
We are required to solve, by factorising, the following equation for .
Now we have two options.













We utilize the periodic property of to find other solutions (roots) of :


Symmetry 

Hence;
Therefore, another solution of is but it is outside desired limit , so we can ignore it.
Since our limits of interest are , we need not to use periodic property of because that will result in solutions outside limits of interest.
We utilize the periodic property of to find another solution (root) of :


Symmetry 
Or

Hence;
Therefore, we have only one solution for .
Since our limits of interest are , we need not to use periodic property of because that will result in solutions outside limits of interest.
Hence there are only two solutions of for .


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