Solve the equation 2cos(3x) -1 = 0 for values in the interval 0=

To solve for x : 2cos(3x)-1 =
0.

x should be in (0, pi)
interval.

Solution:

2cos3x-1 =
0.

=> 2cos3x = 1.

cos3x
= 1/2.

3x = 2npi+pi/3, or 3x=
2npi-pi/3.

=> 3x = pi/3, for n =
0.

So x = pi/9 which is a solution in 0 < x<
= pi.

When n=1, 3x = 2pi+pi/3 , or x=
2pi-pi/3.

So x = 7p/9 , or x=
5pi/9.

Therefore x = {pi/9, 5pi/3 and 7pi/3} are the
solutions in (0, pi) interval.