How to solve the equation cos^2x=1/2 using the formula of difference of two squares.

We'll multiply by 2 both
sides:

2(cos x)^2 = 1

We'll
subtract 1 both sides to create the difference of 2 squares to the left
side:

2(cos x)^2 - 1 = 0

We'll
re-write the difference of squares as a product:

2(cos x)^2
- 1 = (sqrt2*cos x - 1)(sqrt2*cos x + 1)

We'll cancel out
theproduct above:

(sqrt2*cos x - 1)(sqrt2*cos x + 1) =
0

We'll set each factor as
zero:

sqrt2*cos x - 1 =
0

We'll add 1 both
sides:

sqrt2*cos x = 1

We'll
divide by sqrt 2:

cos x = 1/sqrt
2

cos x = sqrt 2/2

x = +arccos
(sqrt 2/2) + 2k*pi

x = pi/4 +
2k*pi

x = - pi/4 + 2k*pi

We'll
set the next factor as zero:

sqrt2*cos x + 1 =
0

We'll subtract 1 both
sides:

sqrt2*cos x = -1

cos x
= -1/sqrt 2

x = pi - arccos (sqrt 2/2) +
2k*pi

x = pi - pi/4 + 2k*pi

x
= 3pi/4

The solutions of the equation are:
{pi/4 + 2k*pi}U{3pi/4 + 2k*pi}.