Book demonstration about trigonometric relations

[Bunny-chan]

Homework Statement

[/B]

In the equation between $(3)$ and $(2)$, why does the author says that

? Isn't the trigonometric identity actually

?

2. Homework Equations

The Attempt at a Solution

 

[FactChecker]

You are right, but that doesn't mean that what they say is wrong. In fact it proves that their statements are correct. They want to prove something about the absolute value, so they took the absolute value of both sides.

 

[Bunny-chan]

You are right, but that doesn't mean that what they say is wrong. In fact it proves that their statements are correct. They want to prove something about the absolute value, so they took the absolute value of both sides.

Sorry, I don't understand what you mean. How does it prove his statement is correct?

I wasn't wondering about the absolute values, I was confused about the fact that it should be two times the cosine, not the sine.

 

[FactChecker]

Sorry, I don't understand what you mean. How does it prove his statement is correct?

I wasn't wondering about the absolute values, I was confused about the fact that it should be two times the cosine, not the sine.

It's the same thing. Multiplication is commutative. They just swapped the order of the multiplication.