Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2012  MayJun  (P19709/11)  Q#1
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Question
Solve the equation , for
Solution
i.
We have the equation;
Dividing both sides of the equation by ;
We have the relation , therefore,
To solve this equation, we can substitute . Hence,
Since given interval is , for interval can be found as follows;
Multiplying both sides of the inequality with 2;
Since ;
Hence the given interval for is .
To solve equation for interval ,
Using calculator we can find the values of .
To find all the solutions (roots) of , we utilize the periodic/symmetry property of .


Periodic/Symmetry 
or

Therefore;
For;
















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


Since ;


Therefore;




Hence, all the solutions of the equation within the interval are;


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shakil
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