Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2003  MayJun  (P19709/01)  Q#2
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Question
Find all the values of in the interval which satisfy the equation;
Solution
First we need to manipulate the given equation to write it in a single trigonometric
ratio;
Dividing the entire equation by ;
Using the relation we can rewrite the equation as,
To solve this equation for , we can substitute . Hence,
Since given interval is , for interval can be found as follows;
Multiplying the entire inequality with 3;
Since ;
Hence the given interval for is .
To solve equation for interval ,
Using calculator we can find the value of .
To find all the solutions (roots) of , we utilize the periodic/symmetry property of .


Periodic/Symmetry 
or

Therefore;
For;
















Only following solutions (roots) of the equation are within interval;



Since ;



Therefore;






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



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