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

The general solution for cos(2x)=cos(1/2) is x= 1/4+pin,x=pi-1/4+pin

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

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

x = \frac{1}{4} + πn, x = π - \frac{1}{4} + πn

Solution steps

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

Apply trig inverse properties

2 x = arccos (cos (\frac{1}{2})) + 2 πn, 2 x = 2 π - arccos (cos (\frac{1}{2})) + 2 πn

Solve

2 x = arccos (cos (\frac{1}{2})) + 2 πn : x = \frac{1}{4} + πn

Solve

2 x = 2 π - arccos (cos (\frac{1}{2})) + 2 πn : x = π - \frac{1}{4} + πn

x = \frac{1}{4} + πn, x = π - \frac{1}{4} + πn

2 sin^{2} (x) - 3 sin (x) + 1 = 0, 0 \leq x < 2 π

cos (x) = \frac{3}{10}

5 cos (3 x + 60) = 4

3 sin^{2} (x) = 0

\frac{5 3}{3} cos (x) = 1 + 3 cos (x)

What is the general solution for cos(2x)=cos(1/2) ?
The general solution for cos(2x)=cos(1/2) is x= 1/4+pin,x=pi-1/4+pin