I am currently learning about the Trig addition formula. The book I am reading has a proof for it. The proof is attached here:
However, I have a question about it. What if the values of theta and phi were greater than 90 degrees, or basically so great that you can't fit them in a right triangle. Since the proof relies on right triangles, would it still be legitimate in such a scenario? Can someone please explain? Don't give me another proof, simply explain if the proof in the book is legitimate for the values of theta and phi were greater than 90 degrees. And if not, then give me another proof.
Can you please explain as simply as possible. I am a high school student still learning pre-calculus, without knowledge of rigorous proofs. Can you try to keep the answer simple, and show and explain all your working so that I can understand?