Simplify cos(nθ + θ)

[nasi112]

Hi to all and happy new year (2022).

How to simplify 6.4 to get 6.5?

 

[Dr.Peterson]

I'd want to see the context, in order to know if there is anything special about the variables that they might be using.

 

[nasi112]

The author is trying to convert the solution \(\displaystyle u(r,\theta)\) for a disk of Laplace's Equation which is in terms of Fourier Series to Poisson Integral Formula which is expressed as integral.

 

[nasi112]

Look at this Professor. It may help.




The author wants to get rid of \(\displaystyle \cos n(\theta - \varphi)\). So he did this:



But I cannot figure out how he jumped from 6.4 to 6.5!