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

The general solution for 2cos^2(x)-1-cos(x)=0 is x=2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin

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

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

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) = 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{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

csc (\frac{π}{6})

tan (15 0^{\circ})

tan (\frac{4 π}{3})

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

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

What is the general solution for 2cos^2(x)-1-cos(x)=0 ?
The general solution for 2cos^2(x)-1-cos(x)=0 is x=2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin