Question

Find the general solution of the equation $4{\cos }^{2}x=1$

Answer 1

The given equation is
$4{\cos }^{2}x=1$
$\Rightarrow {\cos }^{2}x=\frac{1}{4}$
$\Rightarrow {\cos }^{2}x={\left(\frac{1}{2}\right)}^2$
${\cos }^{2}x={\left(\cos \frac{\pi }{3}\right)}^2$
$\Rightarrow {\cos }^{2}x={\cos }^2\frac{\pi }{3}$
$x=\frac{\pi }{3}$
$\therefore$ The general solution, $x=n\pi \pm \frac{\pi }{3}$. where $nϵI$.