Solve for a (complex solution)
\left\{\begin{matrix}a=\frac{2ye^{10i-ix}}{e^{-2ix+20i}+1}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}-\frac{5\pi }{2}+10\\a\in \mathrm{C}\text{, }&y=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}-\frac{5\pi }{2}+10\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=\frac{y}{\cos(x-10)}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}-\frac{5\pi }{2}+10\\a\in \mathrm{R}\text{, }&y=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}-\frac{5\pi }{2}+10\end{matrix}\right.
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a\cos(x-10)=y
Swap sides so that all variable terms are on the left hand side.
\cos(x-10)a=y
The equation is in standard form.
\frac{\cos(x-10)a}{\cos(x-10)}=\frac{y}{\cos(x-10)}
Divide both sides by \cos(x-10).
a=\frac{y}{\cos(x-10)}
Dividing by \cos(x-10) undoes the multiplication by \cos(x-10).
a\cos(x-10)=y
Swap sides so that all variable terms are on the left hand side.
\cos(x-10)a=y
The equation is in standard form.
\frac{\cos(x-10)a}{\cos(x-10)}=\frac{y}{\cos(x-10)}
Divide both sides by \cos(x-10).
a=\frac{y}{\cos(x-10)}
Dividing by \cos(x-10) undoes the multiplication by \cos(x-10).
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