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= pi/3+2pin,x=(5pi)/3+2pin,x=2pin

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

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

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

Solution steps

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

Solve by substitution

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

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

cos (x) = 1 : x = 2 πn

Combine all the solutions

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

2 cos (2 x) - 3 cos (x) = 0

sin (2 x) = \frac{3}{5}

- cos (x) = sin (x)

2 cos^{2} (x) + 5 cos (x) - 3 = 0

x, cos (x) = 1

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= pi/3+2pin,x=(5pi)/3+2pin,x=2pin