Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2009  OctNov  (P19709/12)  Q#5
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Question
i. Prove the identity .
ii. Solve the equation for .
Solution
i.
We have the trigonometric identity;
We can rewrite it in two ways;
ii.
To solve the equation
Therefore the given equation can be written as;
We have the trigonometric relation;
To solve this equation for
Using calculator we can find the value of
To find all the solutions (roots) of


Periodic/Symmetry 
or 
Therefore;
For;








Only following solutions (roots) are within the given interval


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