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

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

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cos^2(x)=cos(x)

cos^{2} (x) = cos (x)

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

Solution steps

cos^{2} (x) = cos (x)

Solve by substitution

cos (x) = 1, cos (x) = 0

cos (x) = 1 : x = 2 πn

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Combine all the solutions

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

cot (x) = - 3

csc (\frac{2 π}{3})

cos (x) = \frac{1}{4}

cot (\frac{3 π}{4})

csc (12 0^{\circ})

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