# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2017 | May-Jun | (P2-9709/21) | Q#5

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Question

i.       Express in the form , where and , giving the  value of correct to 2 decimal places.

ii.       Hence solve the equation for .

Solution

i.

We are given the expression; We are required to write it in the form; If and are positive, then; can be written in the form  can be written in the form where, and , , with Considering the given equation, we have following case at hand; can be written in the form Comparing it with given equation Therefore  Therefore;  Finally, we can find , utilizing the equation;    Using calculator we can find that; Therefore; ii.

We are required to solve the equation; As demonstrated in (i), we can write; Therefore; Hence, we need to solve;   Using calculator we can find that; To find the other solution of we utilize the odd/even property of .

 Properties of Domain Range Periodicity  Odd/Even Translation/ Symmetry    We use odd/even property;  Therefore, we have two solutions (roots) of the equation;     To find all the solutions (roots) over the interval , we utilize the periodic property of for both these values of .

Therefore;  Therefore;  For For   For             Hence all the solutions (roots) of the equation for are;  