What is the general solution for 4cos^2(x)+2cos(x)-2=0 ?

The general solution for 4cos^2(x)+2cos(x)-2=0 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin

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4cos^2(x)+2cos(x)-2=0

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

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

Solution steps

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

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

tan (3 x) = 0

2 cos^{2} (θ) = 2 - cos (2 θ)

tan (x) = 2

tan^{2} (x) + tan (x) - 20 = 0

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

What is the general solution for 4cos^2(x)+2cos(x)-2=0 ?
The general solution for 4cos^2(x)+2cos(x)-2=0 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin