Derive the sine sum formula using the geometrical construction given in the figure?
1 Answer
Explanation:
First, construct two additional lines and label the intersections/vertices as follows:
Proceeding, note that from the right triangle
Then, it remains to calculate
From the right triangle
Next, as the sum of the angle of
As
Then, as
Looking at the right triangle
Calculating the cosine of that angle, we obtain
Putting these together, we get our final result:
=FC+AF
=sin(alpha)cos(beta)+cos(alpha)sin(beta)