Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/13) | Q#7

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Question

    i.      Show that the equation  can be expressed as

Where

  ii.      Hence solve the equation   for .

Solution


i.
 

We are given the equation;

We have the trigonometric identity;

From this we can substitute in above equation;

Let ;

 

   ii.
 

We are required to solve the equation

 for .

From (i) we know that given equation can be written as;

Let ;

Now we have two options.

Since;

Using calculator

 

Properties of

Domain

Range

Periodicity

Odd/Even

Translation/

Symmetry

We utilize the odd/even property of   to find other solutions (roots) of :

Odd/Even Property

Hence;

For

For  

For  

For  

Hence all the solutions (roots) of the equation   for  are;

 

 

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