Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 2 (P29709/02)  Year 2003  MayJun  (P29709/02)  Q#4
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Question
i. Show that the equation
Can be written in the form
ii. Hence solve the equation to
For .
Solution
i.
We are given;
We apply following two addition formulae on both sides of given equation.
Therefore;
Since;
ii.
We are required to solve following equation doe .
We have found in (i) that it can be written as;
Let , then;
Now we have two options.






Since , therefore;




Using calculator we can find that 



Properties of 

Domain 

Range 

Periodicity 



Odd/Even 

Translation/ Symmetry 


We utilize the periodicity/symmetry property of to find other solutions (roots) of :
Therefore;
For ;








For ;








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




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