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

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

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-1/2 =cos(2x)

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

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

Solution steps

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

Switch sides

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

General solutions for

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

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

Solve

2 x = \frac{2 π}{3} + 2 πn : x = \frac{π}{3} + πn

Solve

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

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

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

- 1 + tan (x) = sec (x)

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

cos (x) = cos (1)

sin^{2} (2 θ) = 0

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