Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2012  OctNov  (P19709/13)  Q#3
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Question
Solve the equation , for .
Solution
We have the equation;
We have the trigonometric identity;
We can rewrite the identity as;
Therefore;
To solve this equation for , we can substitute .
Hence,
Now we have two options;









Since;





NOT POSSIBLE

Using calculator we can find the values of .
We utilize the symmetry property of to find other solutions (roots) of :


Symmetry 

Hence;
Therefore;
Therefore, we have two solutions (roots) of the equation;


To find all the solutions (roots) of we utilize the periodic property of .


Periodic 
or

Therefore;




For 
For 




For















Hence all the solutions (roots) of the equation for are;


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