Deriving the addition formulae

Trig Refresher

Deriving addition formulae

 

ABD is a triangle on the unit circle.

  

 

    Rotate ABD through angle β

      A → A’
     D → D’

 

 

But AD² = (A’D’)²

  So

Also,

and

Double angles

Multiple Angles

Example

Show that sin3A = 3sinA - 4sin³A

 

Half Angles

Example

Show that

Start by using the cosine double angle formula:

Let α = A/2 , so 2α = A

Substitute