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

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

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

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

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

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

csc^{2} (x) - csc (x) - 2 = 0

sin (a) = \frac{3}{5}

3 sec (x) = - 2

sec^{2} (x) = \frac{4}{3}

sin (θ) = \frac{3}{4}

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