Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2016  MayJun  (P19709/12)  Q#7
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Question
i. Prove the identity .
ii. Hence solve, for , the equation
Solution
i.
We are given the identity;
We have the trigonometric identity;
It can be rearranged as;
Therefore;
We have ;
ii.
We are required to solve the equation;
We have found in (i) that;
Therefore;
Using calculator we can find the value of ;
We utilize the periodic/symmetry property of to find other solutions (roots) of :


Periodic/Symmetry 
or

Therefore;
For;








For only following solutions (roots) are within the given interval ;

