Harmonic Motion in One dimension -- Question in equation derivation

[Futurestar33]

Homework Statement

I am curious as to how the second line in the equation is equal to the third line in the equation. The book my class is using is Taylor and it just skips so many steps. What happens to the sign, I know this must relate to euler in some way I am just not sure how. Thank you

I am just curious as to why and how

Homework Equations

The Attempt at a Solution

 

[SammyS]

Homework Statement

I am curious as to how the second line in the equation is equal to the third line in the equation. The book my class is using is Taylor and it just skips so many steps. What happens to the sign, I know this must relate to euler in some way I am just not sure how. Thank you

I am just curious as to why and how

Homework Equations

The Attempt at a Solution

Hello Futurestar33. Welcome to PF !

Use angle addition/subtraction formula on cos(ωt - δ) .

 

[BiGyElLoWhAt]

http://pages.pacificcoast.net/~cazelais/173/idns-proof.pdf
First identity in the pdf. Enjoi

 

[BiGyElLoWhAt]

I don't see why they include the second line, seems irrelevant since cos(theta) = cos(-theta)

 

[Futurestar33]

Thank you guys