\input amstex

$$\align
\cos x&=\frac{e^{\text{\pmb i}x}+e^{-\text{\pmb i}x}}2\\
\cos (314t) - \cos (650t)=1\;&\Longleftrightarrow\;
\frac{e^{\text{\pmb i}314 t}+e^{-\hbox{\tiny\pmb{i}}314 t}}2
-\frac{e^{\hbox{\tiny\pmb i}650t}+e^{-\hbox{\tiny\pmb i}650t}}2=1\;\Longleftrightarrow\\
&\Longleftrightarrow\;e^{\hbox{\tiny\pmb i}314t}\cdot\biggl\{1-\frac{e^{\hbox{\tiny\pmb i}336t}+e^{-\hbox{\tiny\pmb i}336t}}2\biggr\}=1\;\Longleftrightarrow\\
&\Longleftrightarrow t=0\;\lor\; \biggl[e^{\hbox{\tiny\pmb i}336t}+e^{-\hbox{\tiny\pmb i}336 t}=2\;\Longleftrightarrow (p\equiv e^{\hbox{\tiny\pmb i}336 t})\\
&\Longleftrightarrow p^2-2p-1=0,\quad e^{\hbox{\tiny\pmb i}336 t}=1\pm\sqrt 2\biggr]
\endalign$$
\bye