Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2003 | May-Jun | (P2-9709/02) | Q#4
Question
i. Show that the equation
Can be written in the form
ii. Hence solve the equation to
For .
Solution
i.
We are given;
We apply following two addition formulae on both sides of given equation.
Therefore;
Since;
ii.
We are required to solve following equation doe .
We have found in (i) that it can be written as;
Let , then;
Now we have two options.
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Since , therefore;
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Using calculator we can find that |
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Properties of |
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Domain |
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Range |
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Periodicity |
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Odd/Even |
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Translation/ Symmetry |
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We utilize the periodicity/symmetry property of to find other solutions (roots) of
:
Therefore;
For ;
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For ;
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Only following solutions (roots) are within the given interval ;
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