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

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

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

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

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

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

5 sin (2 x) = 9 tan (x)

3 cot (x - 2) + 3 = 0

sin (2 x) + 3 sin (4 x) = 0

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

2 sin^{2} (θ) = cos (θ) + 1

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