Cosine and Sine of the Sum of Two Angles

angle α

step

1

2

3

4

5

To find the cosine of the sum of two angles α and β.

First, draw them in a circle of radius 1…

C

O

D

α

β

α+β

1

The formulas for

cos(α+β)

and

sin(α+β)

are derived using purely geometric reasoning, avoiding the usual cumbersome algebraic manipulations. Proceed through steps 1–5 to follow the derivation.