Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2019  OctNov  (P19709/13)  Q#7
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Question
i. Show that the equation can be expressed as
Where
ii. Hence solve the equation for .
Solution
i.
We are given the equation;
We have the trigonometric identity;
From this we can substitute in above equation;
Let ;
ii.
We are required to solve the equation
for .
From (i) we know that given equation can be written as;
Let ;
Now we have two options.





Since;

















Using calculator 





Properties of 

Domain 

Range 

Periodicity 



Odd/Even 

Translation/ Symmetry 






We utilize the odd/even property of to find other solutions (roots) of :


Odd/Even Property 

Hence;
For 
For 
For 
For 




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




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