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

The general solution for 2cos^2(x)-1=cos(x) is x=2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin

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

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

x = 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Solution steps

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

Solve by substitution

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

cos (x) = 1 : x = 2 πn

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Combine all the solutions

x = 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

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

csc^{2} (x) + 6 csc (x) - 7 = 0

\frac{sin ( 2 x ) - 1}{3} = - \frac{1}{6}

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

4 cos (x) + 2 = 3

What is the general solution for 2cos^2(x)-1=cos(x) ?
The general solution for 2cos^2(x)-1=cos(x) is x=2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin