Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/12) | 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
Property

or

Therefore;

For;

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

 

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