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

2 sin (x) + 2 = 0

sin (2 x) = 2 sin (x)

sin (x) - 1 = 0

cos (x) = \frac{1}{3}

tan (x) + 1 = 0

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