# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2003 | May-Jun | (P1-9709/01) | Q#2

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Question

Find all the values of in the interval which satisfy the equation; Solution

First we need to manipulate the given equation to write it in a single trigonometric
ratio; Dividing the entire equation by ;   Using the relation we can rewrite the equation as,   To solve this equation for , we can substitute . Hence, Since given interval is , for interval can be found as follows; Multiplying the entire inequality with 3;  Since ; Hence the given interval for is .

To solve equation for interval ,  Using calculator we can find the value of . To find all the solutions (roots) of , we utilize the periodic/symmetry property of . Periodic/Symmetry Property or Therefore;  For;                Only following solutions (roots) of the equation are within interval;   Since ;   Therefore;      Hence, all the solutions of the equation within interval are;   