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

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

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cos(2x)=(-1)/2

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

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

Solution steps

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

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

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

cos (2 x - \frac{π}{6}) = \frac{3}{2}

12 cos^{2} (θ) = 9

sin (\frac{x}{2}) - 1 = 0

sec (\frac{3 x}{2}) = - 2

cos (θ) = - \frac{4}{5}

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