Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/13) | Q#4

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Question

i.       Show that the equation can be expressed as .

ii.       Solve the equation for .

Solution

i.

We have the equation; We have the relation , therefore,    We have the trigonometric identity; We can write it as; Therefore;     ii.

To solve the equation for , as demonstrated in (i), we can write the given equation as; To solve this equation for , we can substitute . Hence,    Now we have two options;        Since;  Using calculator we can find the values of .   NOT POSSIBLE We utilize the symmetry property of to find other solutions (roots) of : Symmetry Property Hence;  Therefore,  Therefore, we have two solutions (roots) of the equation;   To find all the solutions (roots) of we utilize the periodic property of . Periodic Property or Therefore;  For For    For                         Hence all the solutions (roots) of the equation for are;  