Find all solution of the given equation 4 cos2theta 1 0 th

Find all solution of the given equation. 4 cos^2(theta) - 1 = 0 theta = rad Find all solutions of the given equation. sec^2(theta) - 4 = 0 theta = rad

Solution

Solution:

4 (cos²()) -1 = 0

Cos²() = 1/4

Cos() = -1/2 , and Cos() = + 1/2

= Cos^-1 (-1/2) = 2n +2/3 and 2n + 4/3

= Cos^-1 (+1/2) = 2n +/3 and 2n + 5/3

where n = 0, 1 ,2 ... n

(9)

sec²() -4 =0

sec²() = 4

sec() = +/-2

sec() = -2 and =  2n +2/3 and 2n + 4/3

and sec() = 2 and   = 2n +/3 and 2n + 5/3

where n = 0 ,. 2 ,3 ...n