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x\cos(\frac{10\pi }{3})=1
Swap sides so that all variable terms are on the left hand side.
\cos(\frac{10\pi }{3})x=1
The equation is in standard form.
\frac{\cos(\frac{10\pi }{3})x}{\cos(\frac{10\pi }{3})}=\frac{1}{\cos(\frac{10\pi }{3})}
Divide both sides by \cos(\frac{10}{3}\pi ).
x=\frac{1}{\cos(\frac{10\pi }{3})}
Dividing by \cos(\frac{10}{3}\pi ) undoes the multiplication by \cos(\frac{10}{3}\pi ).
x=-2
Divide 1 by \cos(\frac{10}{3}\pi ).