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

The general solution for |cos(x)|= 1/2 is x=(2pi)/3+2pin,x=(4pi)/3+2pin,x= pi/3+2pin,x=(5pi)/3+2pin

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|cos(x)|= 1/2

∣ cos (x) ∣ = \frac{1}{2}

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

∣ cos (x) ∣ = \frac{1}{2}

Solve by substitution

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

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sin^{2} (θ) - cos^{2} (θ) = 0

sec (x) = tan (x) + 1

5 cos (2 x) + 1 = 3 cos (2 x)

2 sin (4 x) + 6 = 5

7 sin (x) tan (x) = - 8 tan (x)

What is the general solution for |cos(x)|= 1/2 ?
The general solution for |cos(x)|= 1/2 is x=(2pi)/3+2pin,x=(4pi)/3+2pin,x= pi/3+2pin,x=(5pi)/3+2pin