# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Feb-Mar | (P1-9709/12) | Q#4

Question

a.   Solve the equation , giving the solution in an exact form.

b.   Solve, by factorising, the equation  for .

Solution

a.

We are given;

b.

We are required to solve, by factorising, the following equation for .

Now we have two options.

We utilize the periodic property of   to find other solutions (roots) of :

 Symmetry Property

Hence;

Therefore, another solution of  is  but it is outside desired limit , so we  can ignore it.

Since our limits of interest are , we need not to use periodic property of  because  that will result in solutions outside limits of interest.

We utilize the periodic property of   to find another solution (root) of :

 Symmetry Property Or

Hence;

Therefore, we have only one solution  for  .

Since our limits of interest are , we need not to use periodic property of   because  that will result in solutions outside limits of interest.

Hence there are only two solutions of  for .