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

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

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

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

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

Solution steps

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

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 = π + 2 πn

Combine all the solutions

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

sin^{2} (x) = 0

sin (x) = \frac{1}{3}

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

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

tan (2 x) = 1

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