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

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SUMMARY

The expression [cos nt - n*sin nt] can be rewritten as [cos (nt + tan^-1 n)] through the application of trigonometric identities. Specifically, the right-hand side expands to cos(nt) * cos(tan^-1 n) - sin(nt) * sin(tan^-1 n). The transformation involves recognizing the relationship between the sine and cosine of the angle tan^-1(n) and applying the cosine addition formula. This method effectively simplifies the original expression into a more manageable form.

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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.

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The Attempt at a Solution

 
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p75213 said:
[cos nt - n*sin nt] as [cos (nt + tan^-1 n)]

there's a factor missing :rolleyes:

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

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

= … ? :wink:​
 
I see what is going on now.
 

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