Sum and Difference Angle Formula Proof (Sine, Cosine)

[@MATHguide]

Here are some helpful resources:
Sum & Difference Angle Formula (Sine, Cosine): Lesson
www.mathguide.com/lessons2/SDA.html
Sum & Difference Angle Formulas: Quizmaster
www.mathguide.com/cgi-bin/quizmasters3/SDA.cgi
Sum & Difference Angle Formula (Tangent): Lesson
www.mathguide.com/lessons2/SDAT.html

[@ahmadnasr3823]

Very useful and helpful
Thnx

[@SomaliMaths]

easy to follow, but I would like to ask 2 questions if i can. 1. Can you please explain the reason of constructing the rectangle? is it just a accidental or....? 2. Why do you choose UNIT CIRCLE for one triangle but no the other? thanx

[@MATHguide]

By choosing the top triangle to have a hypotenuse of length 1, then its legs are cos B and sin B.

[@gullpachaakhter7360]

The hypotenuse of bottom angle 1unit yes or not if yes why we take cos beta why we don't take it 1

[@MATHguide]

The hypotenuse of the bottom triangle is cos B.