Question

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

Answer 1

$4co{s}^{2}x=1$

$co{s}^{2}x=\frac{1}{4}$

$cosx=\frac{\pm 1}{2}$

Now

If $cosx=\frac{1}{2}$

$x=2n\pi +n/3$

and $x=2n\pi +\frac{3\pi }{3}$

Now

If cos x = -1/2

$x=2\frac{n}{3}+2n\pi$

and

x = $\frac{4\pi }{3}+2n\pi$

[where n = 0,1,2,3,4 ----]