Part 3/6:
This formula gives the cosine of the difference of two angles, and intriguingly, it has a similar structure to the addition formula, with the primary difference residing in the sine components.
Proving this formula follows the same geometric reasoning as before, but we note that the cosine terms retain their positive nature while the sine terms change signs.
To derive this formula, you can follow a similar geometric construction and manipulation of lengths derived from sine and cosine definitions.
Deriving the Formulas
To understand how we derive these formulas visually, let's go through the proof process step by step.
Step-by-Step Proof for Addition
- Set up a triangle on a coordinate plane with angles x and y.