What is the general solution for 4cos^{(2)}(x)-4cos(x)+1=0 ?

The general solution for 4cos^{(2)}(x)-4cos(x)+1=0 is x= pi/3+2pin,x=(5pi)/3+2pin

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4cos^{(2)}(x)-4cos(x)+1=0

4 cos^{(2)} (x) - 4 cos (x) + 1 = 0

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

4 cos^{(2)} (x) - 4 cos (x) + 1 = 0

Solve by substitution

cos (x) = \frac{1}{2}

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

3 cos (2 x) = 3 sin (x)

4 cos (\frac{θ}{2}) + 3 = - 2 cos (θ)

8 cos (2 x) - 1 = 2

2 cos (2 x) + 3 = 23

sin (x) cos (2 x) = \frac{1}{2} (1 + sin (x))

What is the general solution for 4cos^{(2)}(x)-4cos(x)+1=0 ?
The general solution for 4cos^{(2)}(x)-4cos(x)+1=0 is x= pi/3+2pin,x=(5pi)/3+2pin