Lesson 49 - Identities and double angles

Identities:

Sin( x + y) = sinxcosy + cosxsiny                   Cos ( x + y)= cosxcosy - sinxsiny

Sin( x - y) = sinxcosy - cosxsiny                    Cos ( x - y)= cosxcosy + sinxsiny

Double Angles:

Sin(2x) = Sin (x + x)
= sinxcosx  +  cosxsinx     (like terms)
 = 2sinxcosx  > same as Sin(2x)

cos(2x) = Cos ( x + x)    
= cosxcosx - sinxsinx                 cos^2x  - sin^2
= cos^2x -sin^2x                     = cos^2x - (1 - cos^2x)
>> = 1 - 2sin^2x                        = cos^2x - 1 + cos^2x
                                                 >> = 2cos^2x - 1