Solve for a
\left\{\begin{matrix}a=\frac{r}{\cos(n\theta )}\text{, }&\theta =0\text{ or }\nexists n_{1}\in \mathrm{Z}\text{ : }n=\frac{\pi n_{1}}{\theta }+\frac{\pi }{2\theta }\\a\in \mathrm{R}\text{, }&r=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }n=\frac{\pi n_{1}}{\theta }+\frac{\pi }{2\theta }\text{ and }\theta \neq 0\end{matrix}\right.
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a\cos(n\theta )=r
Swap sides so that all variable terms are on the left hand side.
\cos(n\theta )a=r
The equation is in standard form.
\frac{\cos(n\theta )a}{\cos(n\theta )}=\frac{r}{\cos(n\theta )}
Divide both sides by \cos(n\theta ).
a=\frac{r}{\cos(n\theta )}
Dividing by \cos(n\theta ) undoes the multiplication by \cos(n\theta ).
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