Part 4/6:
- Using the Pythagorean theorem, we know the lengths can be represented as:
Length a = cos y
Length b = sin y
- Formulate the full length of the opposing side when visualizing a right angle at the vertex, leading to a connection between a and b via:
- C² = A² + B² where A and B represent sides derived from cosine and sine.
- Following Pythagorean identities, you can derive:
- C² = 1 - 2 * cos x * cos y which leads to establishing a relation for cos(x + y).
Step-by-Step Proof for Subtraction
For cosine subtraction, the steps repeat but with a slight change in the signs due to the angle's direction.
Use the previous identities to align with:
- C² = A² + B² again while utilizing sine transformations properly.