What is the general solution for 2cos^2(x)-3cos(x)+1=0 ?

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

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2cos^2(x)-3cos(x)+1=0

2 cos^{2} (x) - 3 cos (x) + 1 = 0

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

Solution steps

2 cos^{2} (x) - 3 cos (x) + 1 = 0

Solve by substitution

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

cos (x) = 1 : x = 2 πn

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

Combine all the solutions

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

sin (x) = cos (2 x)

cos^{3} (x) = cos (x)

2 cos (x) = 1

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

2 sec^{2} (x) + tan^{2} (x) - 3 = 0

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