[cos nt - n.sin nt] rewrite as [cos (nt + tan^-1 n)]

[p75213]

Homework Statement

I am working through an example in Fourier analysis and the author has rewritten [cos nt - n*sin nt] as [cos (nt + tan^-1 n)]. Can somebody show how he does this? ie. the steps involved.

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

[cos nt - n*sin nt] as [cos (nt + tan^-1 n)]

there's a factor missing

the RHS is cosnt*costan^-1n - sinnt*sintan^-1n

= cosnt*costan^-1n*(1 - sinnt*tantan^-1n)

= … ? ​

 

[p75213]

I see what is going on now.