# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | May-Jun | (P1-9709/11) | Q#1

Question

Solve the equation , for

Solution

i.

We have the equation;

Dividing both sides of the equation by ;

We have the relation , therefore,

To solve this equation, we can substitute . Hence,

Since given interval is  , for  interval can be found as follows;

Multiplying both sides of the inequality with 2;

Since ;

Hence the given interval for  is .

To solve    equation for interval ,

Using calculator we can find the values 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) are within the given interval ;

Since ;

Therefore;

Hence, all the solutions of the equation  within the interval  are;