# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/23) | Q#6

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Question

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

ii.       Hence solve the equation Giving all solutions in the interval .

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 for 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, we need to solve;   Using calculator we can find that;    We utilize the symmetry property of to find another solution (root) of :

 Properties of Domain Range Odd/Even Periodicity  Translation/ Symmetry    Hence;  Therefore;       